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Flat knot 5.109

Min(phi) over symmetries of the knot is: [-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Flat knots (up to 7 crossings) with same phi are :['5.109']
Arrow polynomial of the knot is: 1
Flat knots (up to 7 crossings) with same arrow polynomial are :['4.4', '4.9', '5.13', '5.63', '5.95', '5.109', '5.112', '5.113', '5.114', '5.120', '6.57', '6.60', '6.68', '6.109', '6.127', '6.131', '6.138', '6.230', '6.299', '6.305', '6.307', '6.344', '6.396', '6.403', '6.454', '6.549', '6.585', '6.587', '6.605', '6.664', '6.761', '6.830', '6.884', '6.889', '6.916', '6.939', '6.963', '6.1009', '6.1103', '6.1104', '6.1113', '6.1118', '6.1119', '6.1127', '6.1187', '6.1194', '6.1204', '6.1265', '6.1266', '6.1272', '6.1328', '6.1329', '6.1352', '6.1361', '6.1381', '6.1397', '6.1398', '6.1406', '6.1408', '6.1414', '6.1461', '6.1463', '6.1467', '6.1480', '6.1486', '6.1584', '6.1636', '6.1659', '6.1742', '6.1750', '6.1769', '6.1782', '6.1785', '6.1795', '6.1804', '6.1829', '6.1842', '6.1843', '6.1879', '6.1880', '6.1892', '6.1893', '6.1913', '6.1939', '6.1953', '6.1976', '6.1977', '6.1978', '6.1979', '6.1980', '6.1981', '6.1982', '6.1983', '6.1984', '6.1985', '6.1986', '6.1987', '6.1988', '6.1989', '6.1990', '6.1991', '6.1992', '6.1993', '6.2023', '6.2024', '6.2025', '6.2026', '6.2027', '6.2028', '6.2029', '6.2030', '6.2031', '6.2056', '6.2059', '6.2085', '6.2086', '7.326', '7.340', '7.354', '7.366', '7.678', '7.687', '7.768', '7.838', '7.854', '7.930', '7.932', '7.1701', '7.1707', '7.1772', '7.2226', '7.2254', '7.2270', '7.2285', '7.2290', '7.2577', '7.2946', '7.2978', '7.2985', '7.3315', '7.3364', '7.3367', '7.3715', '7.4208', '7.4686', '7.5440', '7.5799', '7.5806', '7.5810', '7.5812', '7.5952', '7.6185', '7.8483', '7.8707', '7.9668', '7.9689', '7.9696', '7.9710', '7.9927', '7.9942', '7.10099', '7.10101', '7.10210', '7.10237', '7.10363', '7.10388', '7.10390', '7.10421', '7.10638', '7.10644', '7.10760', '7.11715', '7.11718', '7.12303', '7.12743', '7.12856', '7.12975', '7.13427', '7.13436', '7.13442', '7.13474', '7.13608', '7.13705', '7.13890', '7.14274', '7.14884', '7.15092', '7.15108', '7.15130', '7.15583', '7.15630', '7.15640', '7.15648', '7.15661', '7.15706', '7.15958', '7.16007', '7.16074', '7.16112', '7.16121', '7.16146', '7.16167', '7.16188', '7.16210', '7.17168', '7.17282', '7.17442', '7.17500', '7.17727', '7.17853', '7.17859', '7.17861', '7.17863', '7.17927', '7.17992', '7.17999', '7.18003', '7.18005', '7.18014', '7.18058', '7.18060', '7.18137', '7.18596', '7.18605', '7.18606', '7.18609', '7.18682', '7.18684', '7.18961', '7.18963', '7.19132', '7.19135', '7.19142', '7.19144', '7.19202', '7.19272', '7.19379', '7.19381', '7.19413', '7.19471', '7.19686', '7.19769', '7.19778', '7.20365', '7.20425', '7.20427', '7.20657', '7.21741', '7.21785', '7.23092', '7.23116', '7.23364', '7.23454', '7.23508', '7.23642', '7.23661', '7.23731', '7.24147', '7.24285', '7.24443', '7.24766', '7.24794', '7.24851', '7.24855', '7.25030', '7.25336', '7.25526', '7.25624', '7.25754', '7.25757', '7.25874', '7.25877', '7.25901', '7.25940', '7.25942', '7.25962', '7.26054', '7.26114', '7.26117', '7.26368', '7.26438', '7.26446', '7.26669', '7.26812', '7.26832', '7.26946', '7.26960', '7.26987', '7.26991', '7.27033', '7.27052', '7.27159', '7.27162', '7.27306', '7.27349', '7.27500', '7.27832', '7.28162', '7.28165', '7.28169', '7.28172', '7.28187', '7.28196', '7.28314', '7.28652', '7.28703', '7.29090', '7.29093', '7.29101', '7.29110', '7.29120', '7.29123', '7.29177', '7.29248', '7.29472', '7.29494', '7.29858', '7.29914', '7.30099', '7.30135', '7.30165', '7.30195', '7.30410', '7.30511', '7.30939', '7.31247', '7.31452', '7.31465', '7.31487', '7.31666', '7.31722', '7.31727', '7.31731', '7.32196', '7.32199', '7.32204', '7.32673', '7.32678', '7.32689', '7.32759', '7.32926', '7.33030', '7.33056', '7.33107', '7.33109', '7.33131', '7.33143', '7.33184', '7.33217', '7.33240', '7.33300', '7.33432', '7.33483', '7.33511', '7.33515', '7.33521', '7.33529', '7.33534', '7.33979', '7.34055', '7.34195', '7.34257', '7.34420', '7.34428', '7.34495', '7.34571', '7.34618', '7.35222', '7.35223', '7.35224', '7.35237', '7.35246', '7.35250', '7.35261', '7.35270', '7.35278', '7.35280', '7.35282', '7.35287', '7.35289', '7.35291', '7.35295', '7.35299', '7.35314', '7.35316', '7.35329', '7.35333', '7.35462', '7.35464', '7.35475', '7.35478', '7.35485', '7.35487', '7.35534', '7.35580', '7.35638', '7.35649', '7.35651', '7.35652', '7.35653', '7.35659', '7.35668', '7.35669', '7.35673', '7.35678', '7.35679', '7.35714', '7.35717', '7.35723', '7.35737', '7.35933', '7.36183', '7.36228', '7.36248', '7.36251', '7.36252', '7.36435', '7.36459', '7.36488', '7.36492', '7.36537', '7.36539', '7.36591', '7.36690', '7.36777', '7.36780', '7.36781', '7.36790', '7.36818', '7.36933', '7.36942', '7.36974', '7.37019', '7.37043', '7.37044', '7.37065', '7.37069', '7.37072', '7.37076', '7.37091', '7.37093', '7.37098', '7.37099', '7.37103', '7.37107', '7.37109', '7.37110', '7.37114', '7.37135', '7.37174', '7.37366', '7.37536', '7.37566', '7.37585', '7.37788', '7.37799', '7.37900', '7.37907', '7.37916', '7.38308', '7.38408', '7.39025', '7.39067', '7.39087', '7.39091', '7.39141', '7.39158', '7.39243', '7.39244', '7.39383', '7.39389', '7.39470', '7.39509', '7.39522', '7.39700', '7.39701', '7.39722', '7.39723', '7.40007', '7.40190', '7.40637', '7.40779', '7.40840', '7.40854', '7.40872', '7.40988', '7.41124', '7.41223', '7.41243', '7.41299', '7.41304', '7.41306', '7.41346', '7.41568', '7.41570', '7.41571', '7.41574', '7.41578', '7.41583', '7.41587', '7.41648', '7.41672', '7.41705', '7.41729', '7.41757', '7.41767', '7.41772', '7.41775', '7.41867', '7.41887', '7.41939', '7.42071', '7.42089', '7.42091', '7.42092', '7.42104', '7.42109', '7.42133', '7.42153', '7.42292', '7.42296', '7.42313', '7.42393', '7.42396', '7.42596', '7.42597', '7.42611', '7.42746', '7.42748', '7.42749', '7.42840', '7.42913', '7.42946', '7.43152', '7.43157', '7.43160', '7.43171', '7.43174', '7.43185', '7.43191', '7.43198', '7.43348', '7.43401', '7.43409', '7.43425', '7.43617', '7.43659', '7.43660', '7.43661', '7.43665', '7.43672', '7.43684', '7.43714', '7.43865', '7.43924', '7.43943', '7.43948', '7.44077', '7.44246', '7.44332', '7.44347', '7.44362', '7.44373', '7.44381', '7.44397', '7.44400', '7.44512', '7.44520', '7.44545', '7.44586', '7.44637', '7.44658', '7.44668', '7.44675', '7.44727', '7.44731', '7.44745', '7.44753', '7.44754', '7.44806', '7.44807', '7.44836', '7.44857', '7.44867', '7.44871', '7.44878', '7.44936', '7.44965', '7.44974', '7.44981', '7.45043', '7.45048', '7.45073', '7.45089', '7.45146', '7.45177', '7.45182', '7.45189', '7.45190', '7.45191', '7.45192', '7.45193', '7.45194', '7.45195', '7.45196', '7.45197', '7.45198', '7.45199', '7.45200', '7.45201', '7.45202', '7.45203', '7.45204', '7.45205', '7.45206', '7.45207', '7.45208', '7.45209', '7.45210', '7.45211', '7.45212', '7.45213', '7.45214', '7.45215', '7.45216', '7.45217', '7.45218', '7.45219', '7.45220', '7.45221', '7.45222', '7.45223', '7.45224', '7.45225', '7.45226', '7.45227', '7.45228', '7.45229', '7.45230', '7.45231', '7.45232', '7.45233', '7.45234', '7.45235', '7.45236', '7.45237', '7.45238', '7.45239', '7.45240', '7.45241', '7.45242', '7.45243', '7.45244', '7.45245', '7.45246', '7.45247', '7.45248', '7.45249', '7.45250', '7.45251', '7.45252', '7.45253', '7.45254', '7.45255', '7.45256', '7.45257', '7.45258', '7.45259', '7.45260', '7.45261', '7.45262', '7.45263', '7.45264', '7.45265', '7.45266', '7.45267', '7.45268', '7.45269', '7.45270', '7.45271', '7.45272', '7.45273', '7.45274', '7.45275', '7.45276', '7.45277', '7.45278', '7.45279', '7.45280', '7.45281', '7.45282', '7.45283', '7.45284', '7.45285', '7.45289', '7.45291', '7.45309', '7.45321', '7.45329', '7.45339', '7.45347', '7.45350', '7.45351', '7.45357', '7.45358', '7.45359', '7.45377', '7.45388', '7.45399', '7.45401', '7.45404', '7.45414', '7.45415', '7.45424', '7.45425', '7.45426', '7.45427', '7.45428', '7.45429', '7.45430', '7.45431', '7.45432', '7.45433', '7.45434', '7.45435', '7.45436', '7.45437', '7.45438', '7.45439', '7.45440', '7.45441', '7.45442', '7.45443', '7.45444', '7.45445', '7.45446', '7.45447', '7.45448', '7.45449', '7.45450', '7.45451', '7.45452', '7.45453', '7.45454', '7.45455', '7.45456', '7.45457', '7.45458', '7.45459', '7.45460', '7.45461', '7.45462', '7.45463', '7.45519', '7.45535', '7.45573', '7.45580', '7.45586', '7.45587', '7.45591', '7.45594', '7.45596', '7.45691', '7.45749', '7.45758', '7.45775', '7.45793', '7.45794', '7.45797', '7.45798', '7.45805', '7.45869', '7.45870', '7.45877', '7.45890', '7.45895', '7.45896', '7.45901', '7.45904', '7.45905', '7.45968', '7.46023', '7.46068', '7.46127', '7.46142', '7.46229', '7.46230', '7.46231', '7.46232', '7.46233']
Outer characteristic polynomial of the knot is: t^6+12t^4+19t^2
Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.109', '5.111', '6.1882', '7.22455', '7.41622', '7.45126', '7.45175']
2-strand cable arrow polynomial of the knot is: -128K14 + 128K1*2K2 - 32K2*2 + 30
Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.109']
Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.379', 'vk5.388', 'vk5.509', 'vk5.890', 'vk5.1027', 'vk5.1048', 'vk5.1465', 'vk5.1479', 'vk5.1571', 'vk5.2423']
The R3 orbit of minmal crossing diagrams contains:
The diagrammatic symmetry type of this knot is a.
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: [-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]

Flat knots (up to 7 crossings) with same phi are :['5.109']

Arrow polynomial of the knot is: 1

Flat knots (up to 7 crossings) with same arrow polynomial are :['4.4', '4.9', '5.13', '5.63', '5.95', '5.109', '5.112', '5.113', '5.114', '5.120', '6.57', '6.60', '6.68', '6.109', '6.127', '6.131', '6.138', '6.230', '6.299', '6.305', '6.307', '6.344', '6.396', '6.403', '6.454', '6.549', '6.585', '6.587', '6.605', '6.664', '6.761', '6.830', '6.884', '6.889', '6.916', '6.939', '6.963', '6.1009', '6.1103', '6.1104', '6.1113', '6.1118', '6.1119', '6.1127', '6.1187', '6.1194', '6.1204', '6.1265', '6.1266', '6.1272', '6.1328', '6.1329', '6.1352', '6.1361', '6.1381', '6.1397', '6.1398', '6.1406', '6.1408', '6.1414', '6.1461', '6.1463', '6.1467', '6.1480', '6.1486', '6.1584', '6.1636', '6.1659', '6.1742', '6.1750', '6.1769', '6.1782', '6.1785', '6.1795', '6.1804', '6.1829', '6.1842', '6.1843', '6.1879', '6.1880', '6.1892', '6.1893', '6.1913', '6.1939', '6.1953', '6.1976', '6.1977', '6.1978', '6.1979', '6.1980', '6.1981', '6.1982', '6.1983', '6.1984', '6.1985', '6.1986', '6.1987', '6.1988', '6.1989', '6.1990', '6.1991', '6.1992', '6.1993', '6.2023', '6.2024', '6.2025', '6.2026', '6.2027', '6.2028', '6.2029', '6.2030', '6.2031', '6.2056', '6.2059', '6.2085', '6.2086', '7.326', '7.340', '7.354', '7.366', '7.678', '7.687', '7.768', '7.838', '7.854', '7.930', '7.932', '7.1701', '7.1707', '7.1772', '7.2226', '7.2254', '7.2270', '7.2285', '7.2290', '7.2577', '7.2946', '7.2978', '7.2985', '7.3315', '7.3364', '7.3367', '7.3715', '7.4208', '7.4686', '7.5440', '7.5799', '7.5806', '7.5810', '7.5812', '7.5952', '7.6185', '7.8483', '7.8707', '7.9668', '7.9689', '7.9696', '7.9710', '7.9927', '7.9942', '7.10099', '7.10101', '7.10210', '7.10237', '7.10363', '7.10388', '7.10390', '7.10421', '7.10638', '7.10644', '7.10760', '7.11715', '7.11718', '7.12303', '7.12743', '7.12856', '7.12975', '7.13427', '7.13436', '7.13442', '7.13474', '7.13608', '7.13705', '7.13890', '7.14274', '7.14884', '7.15092', '7.15108', '7.15130', '7.15583', '7.15630', '7.15640', '7.15648', '7.15661', '7.15706', '7.15958', '7.16007', '7.16074', '7.16112', '7.16121', '7.16146', '7.16167', '7.16188', '7.16210', '7.17168', '7.17282', '7.17442', '7.17500', '7.17727', '7.17853', '7.17859', '7.17861', '7.17863', '7.17927', '7.17992', '7.17999', '7.18003', '7.18005', '7.18014', '7.18058', '7.18060', '7.18137', '7.18596', '7.18605', '7.18606', '7.18609', '7.18682', '7.18684', '7.18961', '7.18963', '7.19132', '7.19135', '7.19142', '7.19144', '7.19202', '7.19272', '7.19379', '7.19381', '7.19413', '7.19471', '7.19686', '7.19769', '7.19778', '7.20365', '7.20425', '7.20427', '7.20657', '7.21741', '7.21785', '7.23092', '7.23116', '7.23364', '7.23454', '7.23508', '7.23642', '7.23661', '7.23731', '7.24147', '7.24285', '7.24443', '7.24766', '7.24794', '7.24851', '7.24855', '7.25030', '7.25336', '7.25526', '7.25624', '7.25754', '7.25757', '7.25874', '7.25877', '7.25901', '7.25940', '7.25942', '7.25962', '7.26054', '7.26114', '7.26117', '7.26368', '7.26438', '7.26446', '7.26669', '7.26812', '7.26832', '7.26946', '7.26960', '7.26987', '7.26991', '7.27033', '7.27052', '7.27159', '7.27162', '7.27306', '7.27349', '7.27500', '7.27832', '7.28162', '7.28165', '7.28169', '7.28172', '7.28187', '7.28196', '7.28314', '7.28652', '7.28703', '7.29090', '7.29093', '7.29101', '7.29110', '7.29120', '7.29123', '7.29177', '7.29248', '7.29472', '7.29494', '7.29858', '7.29914', '7.30099', '7.30135', '7.30165', '7.30195', '7.30410', '7.30511', '7.30939', '7.31247', '7.31452', '7.31465', '7.31487', '7.31666', '7.31722', '7.31727', '7.31731', '7.32196', '7.32199', '7.32204', '7.32673', '7.32678', '7.32689', '7.32759', '7.32926', '7.33030', '7.33056', '7.33107', '7.33109', '7.33131', '7.33143', '7.33184', '7.33217', '7.33240', '7.33300', '7.33432', '7.33483', '7.33511', '7.33515', '7.33521', '7.33529', '7.33534', '7.33979', '7.34055', '7.34195', '7.34257', '7.34420', '7.34428', '7.34495', '7.34571', '7.34618', '7.35222', '7.35223', '7.35224', '7.35237', '7.35246', '7.35250', '7.35261', '7.35270', '7.35278', '7.35280', '7.35282', '7.35287', '7.35289', '7.35291', '7.35295', '7.35299', '7.35314', '7.35316', '7.35329', '7.35333', '7.35462', '7.35464', '7.35475', '7.35478', '7.35485', '7.35487', '7.35534', '7.35580', '7.35638', '7.35649', '7.35651', '7.35652', '7.35653', '7.35659', '7.35668', '7.35669', '7.35673', '7.35678', '7.35679', '7.35714', '7.35717', '7.35723', '7.35737', '7.35933', '7.36183', '7.36228', '7.36248', '7.36251', '7.36252', '7.36435', '7.36459', '7.36488', '7.36492', '7.36537', '7.36539', '7.36591', '7.36690', '7.36777', '7.36780', '7.36781', '7.36790', '7.36818', '7.36933', '7.36942', '7.36974', '7.37019', '7.37043', '7.37044', '7.37065', '7.37069', '7.37072', '7.37076', '7.37091', '7.37093', '7.37098', '7.37099', '7.37103', '7.37107', '7.37109', '7.37110', '7.37114', '7.37135', '7.37174', '7.37366', '7.37536', '7.37566', '7.37585', '7.37788', '7.37799', '7.37900', '7.37907', '7.37916', '7.38308', '7.38408', '7.39025', '7.39067', '7.39087', '7.39091', '7.39141', '7.39158', '7.39243', '7.39244', '7.39383', '7.39389', '7.39470', '7.39509', '7.39522', '7.39700', '7.39701', '7.39722', '7.39723', '7.40007', '7.40190', '7.40637', '7.40779', '7.40840', '7.40854', '7.40872', '7.40988', '7.41124', '7.41223', '7.41243', '7.41299', '7.41304', '7.41306', '7.41346', '7.41568', '7.41570', '7.41571', '7.41574', '7.41578', '7.41583', '7.41587', '7.41648', '7.41672', '7.41705', '7.41729', '7.41757', '7.41767', '7.41772', '7.41775', '7.41867', '7.41887', '7.41939', '7.42071', '7.42089', '7.42091', '7.42092', '7.42104', '7.42109', '7.42133', '7.42153', '7.42292', '7.42296', '7.42313', '7.42393', '7.42396', '7.42596', '7.42597', '7.42611', '7.42746', '7.42748', '7.42749', '7.42840', '7.42913', '7.42946', '7.43152', '7.43157', '7.43160', '7.43171', '7.43174', '7.43185', '7.43191', '7.43198', '7.43348', '7.43401', '7.43409', '7.43425', '7.43617', '7.43659', '7.43660', '7.43661', '7.43665', '7.43672', '7.43684', '7.43714', '7.43865', '7.43924', '7.43943', '7.43948', '7.44077', '7.44246', '7.44332', '7.44347', '7.44362', '7.44373', '7.44381', '7.44397', '7.44400', '7.44512', '7.44520', '7.44545', '7.44586', '7.44637', '7.44658', '7.44668', '7.44675', '7.44727', '7.44731', '7.44745', '7.44753', '7.44754', '7.44806', '7.44807', '7.44836', '7.44857', '7.44867', '7.44871', '7.44878', '7.44936', '7.44965', '7.44974', '7.44981', '7.45043', '7.45048', '7.45073', '7.45089', '7.45146', '7.45177', '7.45182', '7.45189', '7.45190', '7.45191', '7.45192', '7.45193', '7.45194', '7.45195', '7.45196', '7.45197', '7.45198', '7.45199', '7.45200', '7.45201', '7.45202', '7.45203', '7.45204', '7.45205', '7.45206', '7.45207', '7.45208', '7.45209', '7.45210', '7.45211', '7.45212', '7.45213', '7.45214', '7.45215', '7.45216', '7.45217', '7.45218', '7.45219', '7.45220', '7.45221', '7.45222', '7.45223', '7.45224', '7.45225', '7.45226', '7.45227', '7.45228', '7.45229', '7.45230', '7.45231', '7.45232', '7.45233', '7.45234', '7.45235', '7.45236', '7.45237', '7.45238', '7.45239', '7.45240', '7.45241', '7.45242', '7.45243', '7.45244', '7.45245', '7.45246', '7.45247', '7.45248', '7.45249', '7.45250', '7.45251', '7.45252', '7.45253', '7.45254', '7.45255', '7.45256', '7.45257', '7.45258', '7.45259', '7.45260', '7.45261', '7.45262', '7.45263', '7.45264', '7.45265', '7.45266', '7.45267', '7.45268', '7.45269', '7.45270', '7.45271', '7.45272', '7.45273', '7.45274', '7.45275', '7.45276', '7.45277', '7.45278', '7.45279', '7.45280', '7.45281', '7.45282', '7.45283', '7.45284', '7.45285', '7.45289', '7.45291', '7.45309', '7.45321', '7.45329', '7.45339', '7.45347', '7.45350', '7.45351', '7.45357', '7.45358', '7.45359', '7.45377', '7.45388', '7.45399', '7.45401', '7.45404', '7.45414', '7.45415', '7.45424', '7.45425', '7.45426', '7.45427', '7.45428', '7.45429', '7.45430', '7.45431', '7.45432', '7.45433', '7.45434', '7.45435', '7.45436', '7.45437', '7.45438', '7.45439', '7.45440', '7.45441', '7.45442', '7.45443', '7.45444', '7.45445', '7.45446', '7.45447', '7.45448', '7.45449', '7.45450', '7.45451', '7.45452', '7.45453', '7.45454', '7.45455', '7.45456', '7.45457', '7.45458', '7.45459', '7.45460', '7.45461', '7.45462', '7.45463', '7.45519', '7.45535', '7.45573', '7.45580', '7.45586', '7.45587', '7.45591', '7.45594', '7.45596', '7.45691', '7.45749', '7.45758', '7.45775', '7.45793', '7.45794', '7.45797', '7.45798', '7.45805', '7.45869', '7.45870', '7.45877', '7.45890', '7.45895', '7.45896', '7.45901', '7.45904', '7.45905', '7.45968', '7.46023', '7.46068', '7.46127', '7.46142', '7.46229', '7.46230', '7.46231', '7.46232', '7.46233']

Outer characteristic polynomial of the knot is: t^6+12t^4+19t^2

Flat knots (up to 7 crossings) with same outer characteristic polynomial are :['5.109', '5.111', '6.1882', '7.22455', '7.41622', '7.45126', '7.45175']

2-strand cable arrow polynomial of the knot is: -128*K1**4 + 128*K1**2*K2 - 32*K2**2 + 30

Flat knots (up to 6 crossings) with same 2-strand cable arrow polynomial are :['5.109']

Virtual knots (up to 6 crossings) projecting to this knot are :'vk5.379', 'vk5.388', 'vk5.509', 'vk5.890', 'vk5.1027', 'vk5.1048', 'vk5.1465', 'vk5.1479', 'vk5.1571', 'vk5.2423']

The R3 orbit of minmal crossing diagrams contains:

The diagrammatic symmetry type of this knot is a.

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

Or click here to check the fillings

invariant	value
Gauss code	O1O2U3O4O5U2U1O3U5U4
R3 orbit	{'O1O2U3O4U1O3U5U4O5U2', 'O1O2U3O4O5U2U1O3U5U4', 'O1O2U1O3U4U3O5U2O4U5'}
R3 orbit length	3
Gauss code of -K	Same
Gauss code of K*	Same
Gauss code of -K*	Same
Diagrammatic symmetry type	a
Flat genus of the diagram	2
If K is checkerboard colorable	False
If K is almost classical	False
Based matrix from Gauss code	[[ 0 -1 -1 0 1 1],[ 1 0 0 0 2 1],[ 1 0 0 1 1 0],[ 0 0 -1 0 0 1],[-1 -2 -1 0 0 0],[-1 -1 0 -1 0 0]]
Primitive based matrix	[[ 0 1 1 0 -1 -1],[-1 0 0 0 -1 -2],[-1 0 0 -1 0 -1],[ 0 0 1 0 -1 0],[ 1 1 0 1 0 0],[ 1 2 1 0 0 0]]
If based matrix primitive	True
Phi of primitive based matrix	[-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Phi over symmetry	[-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Phi of -K	[-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Phi of K*	[-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Phi of -K*	[-1,-1,0,1,1,0,0,1,2,1,0,1,1,0,0]
Symmetry type of based matrix	a
u-polynomial	0
Normalized Jones-Krushkal polynomial	-5z-9
Enhanced Jones-Krushkal polynomial	-5w^2z-9w
Inner characteristic polynomial	t^5+8t^3+11t
Outer characteristic polynomial	t^6+12t^4+19t^2
Flat arrow polynomial	1
2-strand cable arrow polynomial	-128K14 + 128K1*2K2 - 32K2*2 + 30
Genus of based matrix	0
Fillings of based matrix	[[{2, 5}, {1, 4}, {3}]]
If K is slice	True

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