Invariant Table Check a Knot Higher Crossing Crossref Virtual Knots Please cite FlatKnotInfo

Flat knot 4.7

Min(phi) over symmetries of the knot is: [-2,-1,1,2,0,1,3,0,1,0]
Flat knots (up to 7 crossings) with same phi are :['4.7', '5.62']
Arrow polynomial of the knot is: -4K12 + 2K2 + 3
Flat knots (up to 7 crossings) with same arrow polynomial are :['4.5', '4.7', '4.10', '4.11', '6.142', '6.563', '6.606', '6.788', '6.892', '6.944', '6.949', '6.971', '6.1011', '6.1060', '6.1124', '6.1212', '6.1238', '6.1241', '6.1274', '6.1291', '6.1304', '6.1309', '6.1312', '6.1373', '6.1390', '6.1392', '6.1393', '6.1394', '6.1403', '6.1407', '6.1412', '6.1413', '6.1423', '6.1424', '6.1425', '6.1426', '6.1438', '6.1440', '6.1448', '6.1449', '6.1452', '6.1453', '6.1456', '6.1457', '6.1478', '6.1479', '6.1520', '6.1554', '6.1559', '6.1588', '6.1589', '6.1609', '6.1610', '6.1619', '6.1621', '6.1626', '6.1630', '6.1632', '6.1633', '6.1643', '6.1657', '6.1689', '6.1721', '6.1723', '6.1737', '6.1764', '6.1777', '6.1783', '6.1808', '6.1816', '6.1853', '6.1855', '6.1856', '6.1860', '6.1864', '6.1871', '6.1872', '6.1875', '6.1882', '6.1891', '6.1894', '6.1895', '6.1896', '6.1897', '6.1898', '6.1900', '6.1902', '6.1903', '6.1938', '6.1940', '6.1942', '6.1946', '6.1947', '6.1952', '6.1956', '6.1957', '6.1959', '6.1965', '6.1968', '6.1969', '6.1970', '6.1972', '6.1973', '6.1974', '6.2000', '6.2006', '6.2012', '6.2032', '6.2033', '6.2035', '6.2036', '6.2037', '6.2038', '6.2040', '6.2041', '6.2042', '6.2044', '6.2045', '6.2047', '6.2048', '6.2049', '6.2052', '6.2053', '6.2054', '6.2055', '6.2058', '6.2060', '6.2061', '6.2062', '6.2067', '6.2069', '6.2072', '6.2073', '6.2076', '6.2077', '6.2080']
Outer characteristic polynomial of the knot is: t^5+21t^3+5t
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.7']
2-strand cable arrow polynomial of the knot is: -64K14 - 96K1*2K2*2 + 256K1*2K2 - 184K12 + 112K1K2K3 + 16K1K3K4 - 16K2*4 + 16K2*2K4 - 120K22 - 40K3*2 - 12K4**2 + 130
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.7']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.14', 'vk4.21', 'vk4.30', 'vk4.48', 'vk4.59', 'vk4.71', 'vk6.3547', 'vk6.3550', 'vk6.3695', 'vk6.3698', 'vk6.3727', 'vk6.3730', 'vk6.3791', 'vk6.3794', 'vk6.3887', 'vk6.3890', 'vk6.3919', 'vk6.3922', 'vk6.3983', 'vk6.3986', 'vk6.4907', 'vk6.4935', 'vk6.4938', 'vk6.4983', 'vk6.4986', 'vk6.5019', 'vk6.5263', 'vk6.5266', 'vk6.5751', 'vk6.5757', 'vk6.5784', 'vk6.5790', 'vk6.6063', 'vk6.6066', 'vk6.6069', 'vk6.6095', 'vk6.6098', 'vk6.6127', 'vk6.6133', 'vk6.6159', 'vk6.6162', 'vk6.6191', 'vk6.6197', 'vk6.6223', 'vk6.6226', 'vk6.6229', 'vk6.6303', 'vk6.6309', 'vk6.6463', 'vk6.6469', 'vk6.6519', 'vk6.6522', 'vk6.6574', 'vk6.6616', 'vk6.6622', 'vk6.6664', 'vk6.6670', 'vk6.6686', 'vk6.6744', 'vk6.6750', 'vk6.6884', 'vk6.6890', 'vk6.6931', 'vk6.6934', 'vk6.6963', 'vk6.6966', 'vk6.7091', 'vk6.7094', 'vk6.7123', 'vk6.7126', 'vk6.7183', 'vk6.7186', 'vk6.7267', 'vk6.7270', 'vk6.7299', 'vk6.7302', 'vk6.7359', 'vk6.7362', 'vk6.7818', 'vk6.7824', 'vk6.7851', 'vk6.7857', 'vk6.8094', 'vk6.8138', 'vk6.8144', 'vk6.8186', 'vk6.8192', 'vk6.8206', 'vk6.8266', 'vk6.8272', 'vk6.8426', 'vk6.8432', 'vk6.8478', 'vk6.8481', 'vk6.8484', 'vk6.8513', 'vk6.8516', 'vk6.8542', 'vk6.8548', 'vk6.8577', 'vk6.8580', 'vk6.8606', 'vk6.8612', 'vk6.8637', 'vk6.8640', 'vk6.8643', 'vk6.8717', 'vk6.8723', 'vk6.8847', 'vk6.8853', 'vk6.8900', 'vk6.8903', 'vk6.9473', 'vk6.9502', 'vk6.9505', 'vk6.9550', 'vk6.9553', 'vk6.9585', 'vk6.9816', 'vk6.9819', 'vk6.11385', 'vk6.11394', 'vk6.11659', 'vk6.11680', 'vk6.12010', 'vk6.12033', 'vk6.12566', 'vk6.12581', 'vk6.12679', 'vk6.12692', 'vk6.13005', 'vk6.13022', 'vk6.13274', 'vk6.13277', 'vk6.13306', 'vk6.13309', 'vk6.13434', 'vk6.13437', 'vk6.13466', 'vk6.13469', 'vk6.13530', 'vk6.13533', 'vk6.13624', 'vk6.13627', 'vk6.13656', 'vk6.13659', 'vk6.13720', 'vk6.13723', 'vk6.13915', 'vk6.13934', 'vk6.14012', 'vk6.14164', 'vk6.14280', 'vk6.14283', 'vk6.14312', 'vk6.14315', 'vk6.14376', 'vk6.14379', 'vk6.14405', 'vk6.14440', 'vk6.14443', 'vk6.14756', 'vk6.14771', 'vk6.14792', 'vk6.14795', 'vk6.15001', 'vk6.15364', 'vk6.15371', 'vk6.15490', 'vk6.15510', 'vk6.15513', 'vk6.15542', 'vk6.15545', 'vk6.15606', 'vk6.15609', 'vk6.15636', 'vk6.15671', 'vk6.15916', 'vk6.15925', 'vk6.15949', 'vk6.15952', 'vk6.16092', 'vk6.16741', 'vk6.16876', 'vk6.17398', 'vk6.17461', 'vk6.17493', 'vk6.18034', 'vk6.18037', 'vk6.18771', 'vk6.18782', 'vk6.19309', 'vk6.19444', 'vk6.19457', 'vk6.19602', 'vk6.19739', 'vk6.19750', 'vk6.19795', 'vk6.19808', 'vk6.19843', 'vk6.19848', 'vk6.20750', 'vk6.20767', 'vk6.20798', 'vk6.20807', 'vk6.20932', 'vk6.21037', 'vk6.21040', 'vk6.21480', 'vk6.21495', 'vk6.21528', 'vk6.21531', 'vk6.21565', 'vk6.21738', 'vk6.21741', 'vk6.21846', 'vk6.21849', 'vk6.22194', 'vk6.22203', 'vk6.22344', 'vk6.22459', 'vk6.22464', 'vk6.22880', 'vk6.22886', 'vk6.22913', 'vk6.22919', 'vk6.23152', 'vk6.23190', 'vk6.23196', 'vk6.23257', 'vk6.23292', 'vk6.23324', 'vk6.23328', 'vk6.23365', 'vk6.23383', 'vk6.23385', 'vk6.23432', 'vk6.23436', 'vk6.23524', 'vk6.23569', 'vk6.23593', 'vk6.23618', 'vk6.23623', 'vk6.23664', 'vk6.23691', 'vk6.23697', 'vk6.23734', 'vk6.23739', 'vk6.23859', 'vk6.23906', 'vk6.23980', 'vk6.24013', 'vk6.24474', 'vk6.24479', 'vk6.24896', 'vk6.24905', 'vk6.25357', 'vk6.25368', 'vk6.25811', 'vk6.25817', 'vk6.25908', 'vk6.25914', 'vk6.25996', 'vk6.26232', 'vk6.26243', 'vk6.26286', 'vk6.26289', 'vk6.26380', 'vk6.26495', 'vk6.26622', 'vk6.26677', 'vk6.26686', 'vk6.26731', 'vk6.26732', 'vk6.27363', 'vk6.27366', 'vk6.27369', 'vk6.27399', 'vk6.27419', 'vk6.27423', 'vk6.27444', 'vk6.27447', 'vk6.27471', 'vk6.27491', 'vk6.27494', 'vk6.27497', 'vk6.27555', 'vk6.27667', 'vk6.27673', 'vk6.27726', 'vk6.27729', 'vk6.27890', 'vk6.27893', 'vk6.28210', 'vk6.28216', 'vk6.28411', 'vk6.28482', 'vk6.28483', 'vk6.29003', 'vk6.29029', 'vk6.29034', 'vk6.29066', 'vk6.29085', 'vk6.29117', 'vk6.29211', 'vk6.29217', 'vk6.29633', 'vk6.29639', 'vk6.29713', 'vk6.29736', 'vk6.29757', 'vk6.29768', 'vk6.30983', 'vk6.31002', 'vk6.31112', 'vk6.31129', 'vk6.32163', 'vk6.32186', 'vk6.32656', 'vk6.32665', 'vk6.32997', 'vk6.33008', 'vk6.33023', 'vk6.33026', 'vk6.33151', 'vk6.33154', 'vk6.33183', 'vk6.33186', 'vk6.33214', 'vk6.33217', 'vk6.33381', 'vk6.33393', 'vk6.33427', 'vk6.33439', 'vk6.33482', 'vk6.33494', 'vk6.33597', 'vk6.33726', 'vk6.33744', 'vk6.33803', 'vk6.34084', 'vk6.34087', 'vk6.34108', 'vk6.34111', 'vk6.34446', 'vk6.34449', 'vk6.34535', 'vk6.34543', 'vk6.34564', 'vk6.34576', 'vk6.34798', 'vk6.34802', 'vk6.34822', 'vk6.34834', 'vk6.34859', 'vk6.34865', 'vk6.34892', 'vk6.34898', 'vk6.35060', 'vk6.35179', 'vk6.35185', 'vk6.35207', 'vk6.35210', 'vk6.35292', 'vk6.35298', 'vk6.35304', 'vk6.35362', 'vk6.35368', 'vk6.35419', 'vk6.35421', 'vk6.35439', 'vk6.35441', 'vk6.35455', 'vk6.35506', 'vk6.35512', 'vk6.35611', 'vk6.35623', 'vk6.35675', 'vk6.35681', 'vk6.35687', 'vk6.35732', 'vk6.35738', 'vk6.35744', 'vk6.35785', 'vk6.35789', 'vk6.35847', 'vk6.35853', 'vk6.35879', 'vk6.35885', 'vk6.35897', 'vk6.35909', 'vk6.35955', 'vk6.35961', 'vk6.36059', 'vk6.36104', 'vk6.36110', 'vk6.36116', 'vk6.36157', 'vk6.36169', 'vk6.36173', 'vk6.36184', 'vk6.36193', 'vk6.36387', 'vk6.36441', 'vk6.36453', 'vk6.36531', 'vk6.36543', 'vk6.36606', 'vk6.36618', 'vk6.37589', 'vk6.37757', 'vk6.37769', 'vk6.37817', 'vk6.37829', 'vk6.37872', 'vk6.37884', 'vk6.37921', 'vk6.37927', 'vk6.37985', 'vk6.37991', 'vk6.38040', 'vk6.38046', 'vk6.38800', 'vk6.38830', 'vk6.38836', 'vk6.38878', 'vk6.38884', 'vk6.38912', 'vk6.38958', 'vk6.38964', 'vk6.38970', 'vk6.39105', 'vk6.39111', 'vk6.39520', 'vk6.39532', 'vk6.39668', 'vk6.39674', 'vk6.39790', 'vk6.39799', 'vk6.39854', 'vk6.39855', 'vk6.39908', 'vk6.39920', 'vk6.39972', 'vk6.39984', 'vk6.40036', 'vk6.40048', 'vk6.40068', 'vk6.40080', 'vk6.40089', 'vk6.40163', 'vk6.40175', 'vk6.40258', 'vk6.40271', 'vk6.40318', 'vk6.40324', 'vk6.40330', 'vk6.40963', 'vk6.40966', 'vk6.40969', 'vk6.40991', 'vk6.40994', 'vk6.41023', 'vk6.41029', 'vk6.41048', 'vk6.41051', 'vk6.41078', 'vk6.41084', 'vk6.41109', 'vk6.41112', 'vk6.41115', 'vk6.41203', 'vk6.41209', 'vk6.41215', 'vk6.41359', 'vk6.41365', 'vk6.41391', 'vk6.41394', 'vk6.41743', 'vk6.41755', 'vk6.41907', 'vk6.41913', 'vk6.42016', 'vk6.42043', 'vk6.42054', 'vk6.42087', 'vk6.42099', 'vk6.42119', 'vk6.42128', 'vk6.42136', 'vk6.42263', 'vk6.42416', 'vk6.42428', 'vk6.42741', 'vk6.42771', 'vk6.42788', 'vk6.42803', 'vk6.42889', 'vk6.42982', 'vk6.43026', 'vk6.43066', 'vk6.43078', 'vk6.43087', 'vk6.43190', 'vk6.43294', 'vk6.43334', 'vk6.43372', 'vk6.43384', 'vk6.43391', 'vk6.43398', 'vk6.43408', 'vk6.43539', 'vk6.43551', 'vk6.43641', 'vk6.43653', 'vk6.43746', 'vk6.43758', 'vk6.43900', 'vk6.43911', 'vk6.44585', 'vk6.44688', 'vk6.44714', 'vk6.44725', 'vk6.44904', 'vk6.44953', 'vk6.44972', 'vk6.45017', 'vk6.45028', 'vk6.45548', 'vk6.45564', 'vk6.45567', 'vk6.45612', 'vk6.45615', 'vk6.45660', 'vk6.45745', 'vk6.45890', 'vk6.45893', 'vk6.46131', 'vk6.46143', 'vk6.46350', 'vk6.46363', 'vk6.46411', 'vk6.46414', 'vk6.46472', 'vk6.46512', 'vk6.46524', 'vk6.46568', 'vk6.46580', 'vk6.46599', 'vk6.46608', 'vk6.46612', 'vk6.46672', 'vk6.46684', 'vk6.46796', 'vk6.46911', 'vk6.46914', 'vk6.47438', 'vk6.47773', 'vk6.47785', 'vk6.47925', 'vk6.47940', 'vk6.48051', 'vk6.48319', 'vk6.48322', 'vk6.48403', 'vk6.48406', 'vk6.48855', 'vk6.48879', 'vk6.48882', 'vk6.48927', 'vk6.48930', 'vk6.49135', 'vk6.49138', 'vk6.49397', 'vk6.49400', 'vk6.49403', 'vk6.49429', 'vk6.49432', 'vk6.49461', 'vk6.49467', 'vk6.49493', 'vk6.49496', 'vk6.49525', 'vk6.49531', 'vk6.49605', 'vk6.49611', 'vk6.49644', 'vk6.49682', 'vk6.49688', 'vk6.49730', 'vk6.49736', 'vk6.49756', 'vk6.49810', 'vk6.49816', 'vk6.49939', 'vk6.50045', 'vk6.50048', 'vk6.50097', 'vk6.50100', 'vk6.50129', 'vk6.50132', 'vk6.50500', 'vk6.50503', 'vk6.50679', 'vk6.50719', 'vk6.50725', 'vk6.50751', 'vk6.50807', 'vk6.50813', 'vk6.50856', 'vk6.50859', 'vk6.50862', 'vk6.50891', 'vk6.50894', 'vk6.50920', 'vk6.50926', 'vk6.50947', 'vk6.50950', 'vk6.51024', 'vk6.51030', 'vk6.51155', 'vk6.51180', 'vk6.51183', 'vk6.51220', 'vk6.51223', 'vk6.53590', 'vk6.53593', 'vk6.53622', 'vk6.53625', 'vk6.53673', 'vk6.53742', 'vk6.54285', 'vk6.54302', 'vk6.54305', 'vk6.54432', 'vk6.54517', 'vk6.54560', 'vk6.54569', 'vk6.54677', 'vk6.54681', 'vk6.54701', 'vk6.54713', 'vk6.54778', 'vk6.54960', 'vk6.55051', 'vk6.55163', 'vk6.55235', 'vk6.55275', 'vk6.55296', 'vk6.55410', 'vk6.55487', 'vk6.55523', 'vk6.55551', 'vk6.55563', 'vk6.55679', 'vk6.55691', 'vk6.55717', 'vk6.55729', 'vk6.55772', 'vk6.55784', 'vk6.57122', 'vk6.57506', 'vk6.57518', 'vk6.57654', 'vk6.57672', 'vk6.57684', 'vk6.57736', 'vk6.58141', 'vk6.58160', 'vk6.58163', 'vk6.58206', 'vk6.58209', 'vk6.58245', 'vk6.58312', 'vk6.58483', 'vk6.58486', 'vk6.58694', 'vk6.58706', 'vk6.58818', 'vk6.58821', 'vk6.58838', 'vk6.58868', 'vk6.58879', 'vk6.58900', 'vk6.58912', 'vk6.58932', 'vk6.59015', 'vk6.59431', 'vk6.59437', 'vk6.59443', 'vk6.59477', 'vk6.59481', 'vk6.59529', 'vk6.59541', 'vk6.59582', 'vk6.59588', 'vk6.59633', 'vk6.59684', 'vk6.59690', 'vk6.59696', 'vk6.59720', 'vk6.59726', 'vk6.59732', 'vk6.59767', 'vk6.59771', 'vk6.59829', 'vk6.59853', 'vk6.59859', 'vk6.59884', 'vk6.59907', 'vk6.59912', 'vk6.59968', 'vk6.59980', 'vk6.60023', 'vk6.60029', 'vk6.60035', 'vk6.60111', 'vk6.60229', 'vk6.60241', 'vk6.60293', 'vk6.60305', 'vk6.60374', 'vk6.60386', 'vk6.60742', 'vk6.60749', 'vk6.61533', 'vk6.61536', 'vk6.61539', 'vk6.61559', 'vk6.61579', 'vk6.61583', 'vk6.61598', 'vk6.61601', 'vk6.61619', 'vk6.61640', 'vk6.61643', 'vk6.61646', 'vk6.61720', 'vk6.61726', 'vk6.61732', 'vk6.61850', 'vk6.61856', 'vk6.61909', 'vk6.61912', 'vk6.62202', 'vk6.62214', 'vk6.62304', 'vk6.62310', 'vk6.62717', 'vk6.62751', 'vk6.62757', 'vk6.62791', 'vk6.62797', 'vk6.62818', 'vk6.62860', 'vk6.62866', 'vk6.62872', 'vk6.62985', 'vk6.62991', 'vk6.63148', 'vk6.63160', 'vk6.63235', 'vk6.63241', 'vk6.64888', 'vk6.64924', 'vk6.64929', 'vk6.64996', 'vk6.65001', 'vk6.65074', 'vk6.65103', 'vk6.65132', 'vk6.65136', 'vk6.65202', 'vk6.65206', 'vk6.65263', 'vk6.66248', 'vk6.66660', 'vk6.66679', 'vk6.66684', 'vk6.66707', 'vk6.66725', 'vk6.66753', 'vk6.66849', 'vk6.66855', 'vk6.67096', 'vk6.67102', 'vk6.67479', 'vk6.67482', 'vk6.67485', 'vk6.67501', 'vk6.67518', 'vk6.67522', 'vk6.67540', 'vk6.67543', 'vk6.67564', 'vk6.67583', 'vk6.67586', 'vk6.67589', 'vk6.67635', 'vk6.67717', 'vk6.67723', 'vk6.67749', 'vk6.67752', 'vk6.67958', 'vk6.67964', 'vk6.69302', 'vk6.69317', 'vk6.69343', 'vk6.69346', 'vk6.69368', 'vk6.69502', 'vk6.69505', 'vk6.71471', 'vk6.71489', 'vk6.72001', 'vk6.72758', 'vk6.72776', 'vk6.72779', 'vk6.72910', 'vk6.73076', 'vk6.73093', 'vk6.73133', 'vk6.73951', 'vk6.74799', 'vk6.74802', 'vk6.74823', 'vk6.74826', 'vk6.75636', 'vk6.75642', 'vk6.75660', 'vk6.75666', 'vk6.75735', 'vk6.75762', 'vk6.75798', 'vk6.75804', 'vk6.75820', 'vk6.75826', 'vk6.75862', 'vk6.75868', 'vk6.76349', 'vk6.76352', 'vk6.76381', 'vk6.76384', 'vk6.77097', 'vk6.77927', 'vk6.77930', 'vk6.77989', 'vk6.78617', 'vk6.78623', 'vk6.78673', 'vk6.78679', 'vk6.78742', 'vk6.78788', 'vk6.78794', 'vk6.78810', 'vk6.78816', 'vk6.78860', 'vk6.78866', 'vk6.79687', 'vk6.79690', 'vk6.79711', 'vk6.79714', 'vk6.80690', 'vk6.80693', 'vk6.80721', 'vk6.80724', 'vk6.82479', 'vk6.82873', 'vk6.82991', 'vk6.83138', 'vk6.83144', 'vk6.83161', 'vk6.83201', 'vk6.83204', 'vk6.83228', 'vk6.83231', 'vk6.83379', 'vk6.83560', 'vk6.83566', 'vk6.83930', 'vk6.84083', 'vk6.84095', 'vk6.84164', 'vk6.84218', 'vk6.84226', 'vk6.84242', 'vk6.84251', 'vk6.84406', 'vk6.84411', 'vk6.84491', 'vk6.84494', 'vk6.84681', 'vk6.84690', 'vk6.85002', 'vk6.85010', 'vk6.85441', 'vk6.85650', 'vk6.85653', 'vk6.85744', 'vk6.85914', 'vk6.85920', 'vk6.85976', 'vk6.86010', 'vk6.86013', 'vk6.86192', 'vk6.86343', 'vk6.86390', 'vk6.86402', 'vk6.86429', 'vk6.86452', 'vk6.86458', 'vk6.86535', 'vk6.86541', 'vk6.86889', 'vk6.86908', 'vk6.86923', 'vk6.87137', 'vk6.87250', 'vk6.87301', 'vk6.87564', 'vk6.87567', 'vk6.87683', 'vk6.87722', 'vk6.87756', 'vk6.87762', 'vk6.87791', 'vk6.87803', 'vk6.88136', 'vk6.88140', 'vk6.88210', 'vk6.88222', 'vk6.88274', 'vk6.88286', 'vk6.88411', 'vk6.88658', 'vk6.88820', 'vk6.89058', 'vk6.89337', 'vk6.89516', 'vk6.89599', 'vk6.89609', 'vk6.89710', 'vk6.89765', 'vk6.90073']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is -.
The reverse -K is
The mirror image K* is
The fillings (up to the first 10) associated to the algebraic genus:
Or click here to check the fillings

Min(phi) over symmetries of the knot is: [-2,-1,1,2,0,1,3,0,1,0]

Flat knots (up to 7 crossings) with same phi are :['4.7', '5.62']

Arrow polynomial of the knot is: -4*K1**2 + 2*K2 + 3

Flat knots (up to 7 crossings) with same arrow polynomial are :['4.5', '4.7', '4.10', '4.11', '6.142', '6.563', '6.606', '6.788', '6.892', '6.944', '6.949', '6.971', '6.1011', '6.1060', '6.1124', '6.1212', '6.1238', '6.1241', '6.1274', '6.1291', '6.1304', '6.1309', '6.1312', '6.1373', '6.1390', '6.1392', '6.1393', '6.1394', '6.1403', '6.1407', '6.1412', '6.1413', '6.1423', '6.1424', '6.1425', '6.1426', '6.1438', '6.1440', '6.1448', '6.1449', '6.1452', '6.1453', '6.1456', '6.1457', '6.1478', '6.1479', '6.1520', '6.1554', '6.1559', '6.1588', '6.1589', '6.1609', '6.1610', '6.1619', '6.1621', '6.1626', '6.1630', '6.1632', '6.1633', '6.1643', '6.1657', '6.1689', '6.1721', '6.1723', '6.1737', '6.1764', '6.1777', '6.1783', '6.1808', '6.1816', '6.1853', '6.1855', '6.1856', '6.1860', '6.1864', '6.1871', '6.1872', '6.1875', '6.1882', '6.1891', '6.1894', '6.1895', '6.1896', '6.1897', '6.1898', '6.1900', '6.1902', '6.1903', '6.1938', '6.1940', '6.1942', '6.1946', '6.1947', '6.1952', '6.1956', '6.1957', '6.1959', '6.1965', '6.1968', '6.1969', '6.1970', '6.1972', '6.1973', '6.1974', '6.2000', '6.2006', '6.2012', '6.2032', '6.2033', '6.2035', '6.2036', '6.2037', '6.2038', '6.2040', '6.2041', '6.2042', '6.2044', '6.2045', '6.2047', '6.2048', '6.2049', '6.2052', '6.2053', '6.2054', '6.2055', '6.2058', '6.2060', '6.2061', '6.2062', '6.2067', '6.2069', '6.2072', '6.2073', '6.2076', '6.2077', '6.2080']

Outer characteristic polynomial of the knot is: t^5+21t^3+5t

Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['4.7']

2-strand cable arrow polynomial of the knot is: -64*K1**4 - 96*K1**2*K2**2 + 256*K1**2*K2 - 184*K1**2 + 112*K1*K2*K3 + 16*K1*K3*K4 - 16*K2**4 + 16*K2**2*K4 - 120*K2**2 - 40*K3**2 - 12*K4**2 + 130

Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['4.7']

Virtual knots (up to 6 crossings) projecting to this knot are :'vk4.14', 'vk4.21', 'vk4.30', 'vk4.48', 'vk4.59', 'vk4.71', 'vk6.3547', 'vk6.3550', 'vk6.3695', 'vk6.3698', 'vk6.3727', 'vk6.3730', 'vk6.3791', 'vk6.3794', 'vk6.3887', 'vk6.3890', 'vk6.3919', 'vk6.3922', 'vk6.3983', 'vk6.3986', 'vk6.4907', 'vk6.4935', 'vk6.4938', 'vk6.4983', 'vk6.4986', 'vk6.5019', 'vk6.5263', 'vk6.5266', 'vk6.5751', 'vk6.5757', 'vk6.5784', 'vk6.5790', 'vk6.6063', 'vk6.6066', 'vk6.6069', 'vk6.6095', 'vk6.6098', 'vk6.6127', 'vk6.6133', 'vk6.6159', 'vk6.6162', 'vk6.6191', 'vk6.6197', 'vk6.6223', 'vk6.6226', 'vk6.6229', 'vk6.6303', 'vk6.6309', 'vk6.6463', 'vk6.6469', 'vk6.6519', 'vk6.6522', 'vk6.6574', 'vk6.6616', 'vk6.6622', 'vk6.6664', 'vk6.6670', 'vk6.6686', 'vk6.6744', 'vk6.6750', 'vk6.6884', 'vk6.6890', 'vk6.6931', 'vk6.6934', 'vk6.6963', 'vk6.6966', 'vk6.7091', 'vk6.7094', 'vk6.7123', 'vk6.7126', 'vk6.7183', 'vk6.7186', 'vk6.7267', 'vk6.7270', 'vk6.7299', 'vk6.7302', 'vk6.7359', 'vk6.7362', 'vk6.7818', 'vk6.7824', 'vk6.7851', 'vk6.7857', 'vk6.8094', 'vk6.8138', 'vk6.8144', 'vk6.8186', 'vk6.8192', 'vk6.8206', 'vk6.8266', 'vk6.8272', 'vk6.8426', 'vk6.8432', 'vk6.8478', 'vk6.8481', 'vk6.8484', 'vk6.8513', 'vk6.8516', 'vk6.8542', 'vk6.8548', 'vk6.8577', 'vk6.8580', 'vk6.8606', 'vk6.8612', 'vk6.8637', 'vk6.8640', 'vk6.8643', 'vk6.8717', 'vk6.8723', 'vk6.8847', 'vk6.8853', 'vk6.8900', 'vk6.8903', 'vk6.9473', 'vk6.9502', 'vk6.9505', 'vk6.9550', 'vk6.9553', 'vk6.9585', 'vk6.9816', 'vk6.9819', 'vk6.11385', 'vk6.11394', 'vk6.11659', 'vk6.11680', 'vk6.12010', 'vk6.12033', 'vk6.12566', 'vk6.12581', 'vk6.12679', 'vk6.12692', 'vk6.13005', 'vk6.13022', 'vk6.13274', 'vk6.13277', 'vk6.13306', 'vk6.13309', 'vk6.13434', 'vk6.13437', 'vk6.13466', 'vk6.13469', 'vk6.13530', 'vk6.13533', 'vk6.13624', 'vk6.13627', 'vk6.13656', 'vk6.13659', 'vk6.13720', 'vk6.13723', 'vk6.13915', 'vk6.13934', 'vk6.14012', 'vk6.14164', 'vk6.14280', 'vk6.14283', 'vk6.14312', 'vk6.14315', 'vk6.14376', 'vk6.14379', 'vk6.14405', 'vk6.14440', 'vk6.14443', 'vk6.14756', 'vk6.14771', 'vk6.14792', 'vk6.14795', 'vk6.15001', 'vk6.15364', 'vk6.15371', 'vk6.15490', 'vk6.15510', 'vk6.15513', 'vk6.15542', 'vk6.15545', 'vk6.15606', 'vk6.15609', 'vk6.15636', 'vk6.15671', 'vk6.15916', 'vk6.15925', 'vk6.15949', 'vk6.15952', 'vk6.16092', 'vk6.16741', 'vk6.16876', 'vk6.17398', 'vk6.17461', 'vk6.17493', 'vk6.18034', 'vk6.18037', 'vk6.18771', 'vk6.18782', 'vk6.19309', 'vk6.19444', 'vk6.19457', 'vk6.19602', 'vk6.19739', 'vk6.19750', 'vk6.19795', 'vk6.19808', 'vk6.19843', 'vk6.19848', 'vk6.20750', 'vk6.20767', 'vk6.20798', 'vk6.20807', 'vk6.20932', 'vk6.21037', 'vk6.21040', 'vk6.21480', 'vk6.21495', 'vk6.21528', 'vk6.21531', 'vk6.21565', 'vk6.21738', 'vk6.21741', 'vk6.21846', 'vk6.21849', 'vk6.22194', 'vk6.22203', 'vk6.22344', 'vk6.22459', 'vk6.22464', 'vk6.22880', 'vk6.22886', 'vk6.22913', 'vk6.22919', 'vk6.23152', 'vk6.23190', 'vk6.23196', 'vk6.23257', 'vk6.23292', 'vk6.23324', 'vk6.23328', 'vk6.23365', 'vk6.23383', 'vk6.23385', 'vk6.23432', 'vk6.23436', 'vk6.23524', 'vk6.23569', 'vk6.23593', 'vk6.23618', 'vk6.23623', 'vk6.23664', 'vk6.23691', 'vk6.23697', 'vk6.23734', 'vk6.23739', 'vk6.23859', 'vk6.23906', 'vk6.23980', 'vk6.24013', 'vk6.24474', 'vk6.24479', 'vk6.24896', 'vk6.24905', 'vk6.25357', 'vk6.25368', 'vk6.25811', 'vk6.25817', 'vk6.25908', 'vk6.25914', 'vk6.25996', 'vk6.26232', 'vk6.26243', 'vk6.26286', 'vk6.26289', 'vk6.26380', 'vk6.26495', 'vk6.26622', 'vk6.26677', 'vk6.26686', 'vk6.26731', 'vk6.26732', 'vk6.27363', 'vk6.27366', 'vk6.27369', 'vk6.27399', 'vk6.27419', 'vk6.27423', 'vk6.27444', 'vk6.27447', 'vk6.27471', 'vk6.27491', 'vk6.27494', 'vk6.27497', 'vk6.27555', 'vk6.27667', 'vk6.27673', 'vk6.27726', 'vk6.27729', 'vk6.27890', 'vk6.27893', 'vk6.28210', 'vk6.28216', 'vk6.28411', 'vk6.28482', 'vk6.28483', 'vk6.29003', 'vk6.29029', 'vk6.29034', 'vk6.29066', 'vk6.29085', 'vk6.29117', 'vk6.29211', 'vk6.29217', 'vk6.29633', 'vk6.29639', 'vk6.29713', 'vk6.29736', 'vk6.29757', 'vk6.29768', 'vk6.30983', 'vk6.31002', 'vk6.31112', 'vk6.31129', 'vk6.32163', 'vk6.32186', 'vk6.32656', 'vk6.32665', 'vk6.32997', 'vk6.33008', 'vk6.33023', 'vk6.33026', 'vk6.33151', 'vk6.33154', 'vk6.33183', 'vk6.33186', 'vk6.33214', 'vk6.33217', 'vk6.33381', 'vk6.33393', 'vk6.33427', 'vk6.33439', 'vk6.33482', 'vk6.33494', 'vk6.33597', 'vk6.33726', 'vk6.33744', 'vk6.33803', 'vk6.34084', 'vk6.34087', 'vk6.34108', 'vk6.34111', 'vk6.34446', 'vk6.34449', 'vk6.34535', 'vk6.34543', 'vk6.34564', 'vk6.34576', 'vk6.34798', 'vk6.34802', 'vk6.34822', 'vk6.34834', 'vk6.34859', 'vk6.34865', 'vk6.34892', 'vk6.34898', 'vk6.35060', 'vk6.35179', 'vk6.35185', 'vk6.35207', 'vk6.35210', 'vk6.35292', 'vk6.35298', 'vk6.35304', 'vk6.35362', 'vk6.35368', 'vk6.35419', 'vk6.35421', 'vk6.35439', 'vk6.35441', 'vk6.35455', 'vk6.35506', 'vk6.35512', 'vk6.35611', 'vk6.35623', 'vk6.35675', 'vk6.35681', 'vk6.35687', 'vk6.35732', 'vk6.35738', 'vk6.35744', 'vk6.35785', 'vk6.35789', 'vk6.35847', 'vk6.35853', 'vk6.35879', 'vk6.35885', 'vk6.35897', 'vk6.35909', 'vk6.35955', 'vk6.35961', 'vk6.36059', 'vk6.36104', 'vk6.36110', 'vk6.36116', 'vk6.36157', 'vk6.36169', 'vk6.36173', 'vk6.36184', 'vk6.36193', 'vk6.36387', 'vk6.36441', 'vk6.36453', 'vk6.36531', 'vk6.36543', 'vk6.36606', 'vk6.36618', 'vk6.37589', 'vk6.37757', 'vk6.37769', 'vk6.37817', 'vk6.37829', 'vk6.37872', 'vk6.37884', 'vk6.37921', 'vk6.37927', 'vk6.37985', 'vk6.37991', 'vk6.38040', 'vk6.38046', 'vk6.38800', 'vk6.38830', 'vk6.38836', 'vk6.38878', 'vk6.38884', 'vk6.38912', 'vk6.38958', 'vk6.38964', 'vk6.38970', 'vk6.39105', 'vk6.39111', 'vk6.39520', 'vk6.39532', 'vk6.39668', 'vk6.39674', 'vk6.39790', 'vk6.39799', 'vk6.39854', 'vk6.39855', 'vk6.39908', 'vk6.39920', 'vk6.39972', 'vk6.39984', 'vk6.40036', 'vk6.40048', 'vk6.40068', 'vk6.40080', 'vk6.40089', 'vk6.40163', 'vk6.40175', 'vk6.40258', 'vk6.40271', 'vk6.40318', 'vk6.40324', 'vk6.40330', 'vk6.40963', 'vk6.40966', 'vk6.40969', 'vk6.40991', 'vk6.40994', 'vk6.41023', 'vk6.41029', 'vk6.41048', 'vk6.41051', 'vk6.41078', 'vk6.41084', 'vk6.41109', 'vk6.41112', 'vk6.41115', 'vk6.41203', 'vk6.41209', 'vk6.41215', 'vk6.41359', 'vk6.41365', 'vk6.41391', 'vk6.41394', 'vk6.41743', 'vk6.41755', 'vk6.41907', 'vk6.41913', 'vk6.42016', 'vk6.42043', 'vk6.42054', 'vk6.42087', 'vk6.42099', 'vk6.42119', 'vk6.42128', 'vk6.42136', 'vk6.42263', 'vk6.42416', 'vk6.42428', 'vk6.42741', 'vk6.42771', 'vk6.42788', 'vk6.42803', 'vk6.42889', 'vk6.42982', 'vk6.43026', 'vk6.43066', 'vk6.43078', 'vk6.43087', 'vk6.43190', 'vk6.43294', 'vk6.43334', 'vk6.43372', 'vk6.43384', 'vk6.43391', 'vk6.43398', 'vk6.43408', 'vk6.43539', 'vk6.43551', 'vk6.43641', 'vk6.43653', 'vk6.43746', 'vk6.43758', 'vk6.43900', 'vk6.43911', 'vk6.44585', 'vk6.44688', 'vk6.44714', 'vk6.44725', 'vk6.44904', 'vk6.44953', 'vk6.44972', 'vk6.45017', 'vk6.45028', 'vk6.45548', 'vk6.45564', 'vk6.45567', 'vk6.45612', 'vk6.45615', 'vk6.45660', 'vk6.45745', 'vk6.45890', 'vk6.45893', 'vk6.46131', 'vk6.46143', 'vk6.46350', 'vk6.46363', 'vk6.46411', 'vk6.46414', 'vk6.46472', 'vk6.46512', 'vk6.46524', 'vk6.46568', 'vk6.46580', 'vk6.46599', 'vk6.46608', 'vk6.46612', 'vk6.46672', 'vk6.46684', 'vk6.46796', 'vk6.46911', 'vk6.46914', 'vk6.47438', 'vk6.47773', 'vk6.47785', 'vk6.47925', 'vk6.47940', 'vk6.48051', 'vk6.48319', 'vk6.48322', 'vk6.48403', 'vk6.48406', 'vk6.48855', 'vk6.48879', 'vk6.48882', 'vk6.48927', 'vk6.48930', 'vk6.49135', 'vk6.49138', 'vk6.49397', 'vk6.49400', 'vk6.49403', 'vk6.49429', 'vk6.49432', 'vk6.49461', 'vk6.49467', 'vk6.49493', 'vk6.49496', 'vk6.49525', 'vk6.49531', 'vk6.49605', 'vk6.49611', 'vk6.49644', 'vk6.49682', 'vk6.49688', 'vk6.49730', 'vk6.49736', 'vk6.49756', 'vk6.49810', 'vk6.49816', 'vk6.49939', 'vk6.50045', 'vk6.50048', 'vk6.50097', 'vk6.50100', 'vk6.50129', 'vk6.50132', 'vk6.50500', 'vk6.50503', 'vk6.50679', 'vk6.50719', 'vk6.50725', 'vk6.50751', 'vk6.50807', 'vk6.50813', 'vk6.50856', 'vk6.50859', 'vk6.50862', 'vk6.50891', 'vk6.50894', 'vk6.50920', 'vk6.50926', 'vk6.50947', 'vk6.50950', 'vk6.51024', 'vk6.51030', 'vk6.51155', 'vk6.51180', 'vk6.51183', 'vk6.51220', 'vk6.51223', 'vk6.53590', 'vk6.53593', 'vk6.53622', 'vk6.53625', 'vk6.53673', 'vk6.53742', 'vk6.54285', 'vk6.54302', 'vk6.54305', 'vk6.54432', 'vk6.54517', 'vk6.54560', 'vk6.54569', 'vk6.54677', 'vk6.54681', 'vk6.54701', 'vk6.54713', 'vk6.54778', 'vk6.54960', 'vk6.55051', 'vk6.55163', 'vk6.55235', 'vk6.55275', 'vk6.55296', 'vk6.55410', 'vk6.55487', 'vk6.55523', 'vk6.55551', 'vk6.55563', 'vk6.55679', 'vk6.55691', 'vk6.55717', 'vk6.55729', 'vk6.55772', 'vk6.55784', 'vk6.57122', 'vk6.57506', 'vk6.57518', 'vk6.57654', 'vk6.57672', 'vk6.57684', 'vk6.57736', 'vk6.58141', 'vk6.58160', 'vk6.58163', 'vk6.58206', 'vk6.58209', 'vk6.58245', 'vk6.58312', 'vk6.58483', 'vk6.58486', 'vk6.58694', 'vk6.58706', 'vk6.58818', 'vk6.58821', 'vk6.58838', 'vk6.58868', 'vk6.58879', 'vk6.58900', 'vk6.58912', 'vk6.58932', 'vk6.59015', 'vk6.59431', 'vk6.59437', 'vk6.59443', 'vk6.59477', 'vk6.59481', 'vk6.59529', 'vk6.59541', 'vk6.59582', 'vk6.59588', 'vk6.59633', 'vk6.59684', 'vk6.59690', 'vk6.59696', 'vk6.59720', 'vk6.59726', 'vk6.59732', 'vk6.59767', 'vk6.59771', 'vk6.59829', 'vk6.59853', 'vk6.59859', 'vk6.59884', 'vk6.59907', 'vk6.59912', 'vk6.59968', 'vk6.59980', 'vk6.60023', 'vk6.60029', 'vk6.60035', 'vk6.60111', 'vk6.60229', 'vk6.60241', 'vk6.60293', 'vk6.60305', 'vk6.60374', 'vk6.60386', 'vk6.60742', 'vk6.60749', 'vk6.61533', 'vk6.61536', 'vk6.61539', 'vk6.61559', 'vk6.61579', 'vk6.61583', 'vk6.61598', 'vk6.61601', 'vk6.61619', 'vk6.61640', 'vk6.61643', 'vk6.61646', 'vk6.61720', 'vk6.61726', 'vk6.61732', 'vk6.61850', 'vk6.61856', 'vk6.61909', 'vk6.61912', 'vk6.62202', 'vk6.62214', 'vk6.62304', 'vk6.62310', 'vk6.62717', 'vk6.62751', 'vk6.62757', 'vk6.62791', 'vk6.62797', 'vk6.62818', 'vk6.62860', 'vk6.62866', 'vk6.62872', 'vk6.62985', 'vk6.62991', 'vk6.63148', 'vk6.63160', 'vk6.63235', 'vk6.63241', 'vk6.64888', 'vk6.64924', 'vk6.64929', 'vk6.64996', 'vk6.65001', 'vk6.65074', 'vk6.65103', 'vk6.65132', 'vk6.65136', 'vk6.65202', 'vk6.65206', 'vk6.65263', 'vk6.66248', 'vk6.66660', 'vk6.66679', 'vk6.66684', 'vk6.66707', 'vk6.66725', 'vk6.66753', 'vk6.66849', 'vk6.66855', 'vk6.67096', 'vk6.67102', 'vk6.67479', 'vk6.67482', 'vk6.67485', 'vk6.67501', 'vk6.67518', 'vk6.67522', 'vk6.67540', 'vk6.67543', 'vk6.67564', 'vk6.67583', 'vk6.67586', 'vk6.67589', 'vk6.67635', 'vk6.67717', 'vk6.67723', 'vk6.67749', 'vk6.67752', 'vk6.67958', 'vk6.67964', 'vk6.69302', 'vk6.69317', 'vk6.69343', 'vk6.69346', 'vk6.69368', 'vk6.69502', 'vk6.69505', 'vk6.71471', 'vk6.71489', 'vk6.72001', 'vk6.72758', 'vk6.72776', 'vk6.72779', 'vk6.72910', 'vk6.73076', 'vk6.73093', 'vk6.73133', 'vk6.73951', 'vk6.74799', 'vk6.74802', 'vk6.74823', 'vk6.74826', 'vk6.75636', 'vk6.75642', 'vk6.75660', 'vk6.75666', 'vk6.75735', 'vk6.75762', 'vk6.75798', 'vk6.75804', 'vk6.75820', 'vk6.75826', 'vk6.75862', 'vk6.75868', 'vk6.76349', 'vk6.76352', 'vk6.76381', 'vk6.76384', 'vk6.77097', 'vk6.77927', 'vk6.77930', 'vk6.77989', 'vk6.78617', 'vk6.78623', 'vk6.78673', 'vk6.78679', 'vk6.78742', 'vk6.78788', 'vk6.78794', 'vk6.78810', 'vk6.78816', 'vk6.78860', 'vk6.78866', 'vk6.79687', 'vk6.79690', 'vk6.79711', 'vk6.79714', 'vk6.80690', 'vk6.80693', 'vk6.80721', 'vk6.80724', 'vk6.82479', 'vk6.82873', 'vk6.82991', 'vk6.83138', 'vk6.83144', 'vk6.83161', 'vk6.83201', 'vk6.83204', 'vk6.83228', 'vk6.83231', 'vk6.83379', 'vk6.83560', 'vk6.83566', 'vk6.83930', 'vk6.84083', 'vk6.84095', 'vk6.84164', 'vk6.84218', 'vk6.84226', 'vk6.84242', 'vk6.84251', 'vk6.84406', 'vk6.84411', 'vk6.84491', 'vk6.84494', 'vk6.84681', 'vk6.84690', 'vk6.85002', 'vk6.85010', 'vk6.85441', 'vk6.85650', 'vk6.85653', 'vk6.85744', 'vk6.85914', 'vk6.85920', 'vk6.85976', 'vk6.86010', 'vk6.86013', 'vk6.86192', 'vk6.86343', 'vk6.86390', 'vk6.86402', 'vk6.86429', 'vk6.86452', 'vk6.86458', 'vk6.86535', 'vk6.86541', 'vk6.86889', 'vk6.86908', 'vk6.86923', 'vk6.87137', 'vk6.87250', 'vk6.87301', 'vk6.87564', 'vk6.87567', 'vk6.87683', 'vk6.87722', 'vk6.87756', 'vk6.87762', 'vk6.87791', 'vk6.87803', 'vk6.88136', 'vk6.88140', 'vk6.88210', 'vk6.88222', 'vk6.88274', 'vk6.88286', 'vk6.88411', 'vk6.88658', 'vk6.88820', 'vk6.89058', 'vk6.89337', 'vk6.89516', 'vk6.89599', 'vk6.89609', 'vk6.89710', 'vk6.89765', 'vk6.90073']

The R3 orbit of minmal crossing diagrams contains:

The diagrammatic symmetry type of this knot is -.

The reverse -K is

The mirror image K* is

The fillings (up to the first 10) associated to the algebraic genus:

Or click here to check the fillings

invariant	value
Gauss code	O1O2O3U2O4U1U4U3
R3 orbit	{'O1O2O3U2O4U1U4U3'}
R3 orbit length	1
Gauss code of -K	O1O2O3U1U4U3O4U2
Gauss code of K*	O1O2O3U1U4U3O4U2
Gauss code of -K*	Same
Diagrammatic symmetry type	-
Flat genus of the diagram	2
If K is checkerboard colorable	False
If K is almost classical	False
Based matrix from Gauss code	[[ 0 -2 -1 2 1],[ 2 0 0 3 1],[ 1 0 0 1 0],[-2 -3 -1 0 0],[-1 -1 0 0 0]]
Primitive based matrix	[[ 0 2 1 -1 -2],[-2 0 0 -1 -3],[-1 0 0 0 -1],[ 1 1 0 0 0],[ 2 3 1 0 0]]
If based matrix primitive	True
Phi of primitive based matrix	[-2,-1,1,2,0,1,3,0,1,0]
Phi over symmetry	[-2,-1,1,2,0,1,3,0,1,0]
Phi of -K	[-2,-1,1,2,1,2,1,2,2,1]
Phi of K*	[-2,-1,1,2,1,2,1,2,2,1]
Phi of -K*	[-2,-1,1,2,0,1,3,0,1,0]
Symmetry type of based matrix	-
u-polynomial	0
Normalized Jones-Krushkal polynomial	4z+9
Enhanced Jones-Krushkal polynomial	4w^2z+9w
Inner characteristic polynomial	t^4+11t^2+1
Outer characteristic polynomial	t^5+21t^3+5t
Flat arrow polynomial	-4K12 + 2K2 + 3
2-strand cable arrow polynomial	-64K14 - 96K1*2K2*2 + 256K1*2K2 - 184K12 + 112K1K2K3 + 16K1K3K4 - 16K2*4 + 16K2*2K4 - 120K22 - 40K3*2 - 12K4**2 + 130
Genus of based matrix	0
Fillings of based matrix	[[{2, 4}, {1, 3}]]
If K is slice	True

Contact