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ec_curvedata • Show schema
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{'Ciso': '4410bk', 'Clabel': '4410bk5', 'Cnumber': 5, 'abc_quality': 1.0347196629545203, 'absD': 54718349548988380500, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 840, 'ainvs': [1, -1, 1, 847813, 190527999], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 4410, 'degree': 147456, 'elladic_images': ['8.12.0.6', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.4752200808381053332294325767', 'prec': 100}, 'faltings_index': 4, 'faltings_ratio': 4, 'iso_nlabel': 34, 'isogeny_degrees': [1, 2, 3, 4, 6, 12], 'jinv': [785793873833639, 637994920500], 'lmfdb_iso': '4410.bi', 'lmfdb_label': '4410.bi8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 1922, 20756], 'min_quad_twist_disc': 21, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '4.6.0.c.1', '6.12.0.a.1', '8.12.0-4.c.1.5', '12.48.0.c.1', '20.12.0.h.1', '21.8.0-3.a.1.2', '24.96.0-12.c.1.23', '40.24.0-20.h.1.5', '42.24.0-6.a.1.4', '60.96.1.m.4', '84.96.0.?', '120.192.1.?', '168.192.1.?', '420.192.1.?', '840.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.8156069370389626843929937596', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.95295886197639383497913358652', 'prec': 103}, 'szpiro_ratio': 6.263961882370837, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, -2, 0, 0, 1, -6, 0, -8, 1], 'aplist': [1, 0, 1, 0, 0, -2, -6, -8, 0, -6, 4, -10, -6, -4, 0, 6, -12, 10, -4, -12, 10, 8, 12, -6, 10], 'class_deg': 12, 'class_size': 8, 'conductor': 4410, 'isogeny_matrix': [[1, 2, 4, 3, 4, 6, 12, 12], [2, 1, 2, 6, 2, 3, 6, 6], [4, 2, 1, 12, 4, 6, 12, 3], [3, 6, 12, 1, 12, 2, 4, 4], [4, 2, 4, 12, 1, 6, 3, 12], [6, 3, 6, 2, 6, 1, 2, 2], [12, 6, 12, 4, 3, 2, 1, 4], [12, 6, 3, 4, 12, 2, 4, 1]], 'lmfdb_iso': '4410.bi', 'trace_hash': 873694506651951836}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0070802917699819306650049688406', 'prec': 110}, 'conductor': 4410, 'gens': [[387, 23816, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.8156069370389626843929937596', 'prec': 100}], 'lmfdb_label': '4410.bi8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.12838446683357407637775998892', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '5.5942974861860573048886765609624055673', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[-853, 849, 2]], 'xcoord_integral_points': [387, 1427]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 2], '3': 'a', '5': [2, 0], '7': 'a', '11': [1, 1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 1, 0]}, 'iwp0': 0, 'lmfdb_label': '4410.bi8'}
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ec_torsion_growth • Show schema
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id: 230532
{'degree': 2, 'field': [-5, -1, 1], 'lmfdb_label': '4410.bi8', 'torsion': [12]}
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id: 230531
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 2]}
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id: 230533
{'degree': 2, 'field': [105, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [4]}
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id: 230535
{'degree': 4, 'field': [-20, 0, -2, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [24]}
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id: 230534
{'degree': 4, 'field': [105, 0, 1, -2, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 12]}
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id: 230536
{'degree': 6, 'field': [1, -4, 9, 6, -3, -2, 1], 'lmfdb_label': '4410.bi8', 'torsion': [6]}
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id: 230538
{'degree': 8, 'field': [25, 0, 0, 0, 410, 0, 0, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [8]}
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id: 230537
{'degree': 8, 'field': [966, -588, 772, -390, 251, -70, 28, -4, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 4]}
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id: 230539
{'degree': 8, 'field': [2025, 0, -180, 0, 19, 0, 4, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 24]}
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id: 230540
{'degree': 12, 'field': [1, -5, 21, -22, 19, 21, -20, 21, 3, -8, 7, -3, 1], 'lmfdb_label': '4410.bi8', 'torsion': [3, 12]}
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id: 230542
{'degree': 12, 'field': [15316, -11984, 8540, -14560, 3612, 1316, 652, 208, -66, -8, 2, -4, 1], 'lmfdb_label': '4410.bi8', 'torsion': [12]}
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id: 230541
{'degree': 12, 'field': [94816, -23648, 47824, -14720, 12472, -4872, 2780, -840, 388, -76, 28, -4, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 6]}
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id: 230544
{'degree': 16, 'field': [463761, 0, -435612, 0, 172558, 0, -25924, 0, 2475, 0, -164, 0, 138, 0, 8, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [2, 24]}
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id: 230543
{'degree': 16, 'field': [933156, 0, -1145760, 0, 622276, 0, -207220, 0, 48861, 0, -7580, 0, 726, 0, -40, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [4, 12]}
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id: 230545
{'degree': 16, 'field': [39690000, 0, -211680000, 0, 6010200, 0, -1948800, 0, -381800, 0, 5120, 0, 1938, 0, 80, 0, 1], 'lmfdb_label': '4410.bi8', 'torsion': [48]}
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id: 230546
{'degree': 18, 'field': [-675, -78975, 1279800, -10305315, 39408930, -78532470, 87585279, -57187593, 22602348, -6026640, 1589220, -507033, 123751, -20301, 3840, -770, 78, -6, 1], 'lmfdb_label': '4410.bi8', 'torsion': [36]}
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ec_localdata • Show schema
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id: 83798
{'conductor': 4410, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4410.bi8', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 83799
{'conductor': 4410, 'conductor_valuation': 2, 'discriminant_valuation': 18, 'j_denominator_valuation': 12, 'kodaira_symbol': -16, 'lmfdb_label': '4410.bi8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 83800
{'conductor': 4410, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '4410.bi8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 83801
{'conductor': 4410, 'conductor_valuation': 2, 'discriminant_valuation': 10, 'j_denominator_valuation': 4, 'kodaira_symbol': -8, 'lmfdb_label': '4410.bi8', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1692637
{'adelic_gens': [[681, 808, 836, 509], [599, 816, 468, 551], [1, 12, 12, 145], [352, 3, 717, 754], [15, 106, 374, 11], [646, 21, 345, 466], [817, 24, 816, 25], [1, 24, 0, 1], [419, 816, 268, 691], [1, 0, 24, 1]], 'adelic_image': '840.384.5.?', 'conductor': 4410, 'lmfdb_label': '4410.bi8', 'prime': 0}
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id: 21875
{'conductor': 4410, 'elladic_image': '8.12.0.6', 'lmfdb_label': '4410.bi8', 'modell_image': '2B', 'prime': 2}
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id: 21876
{'conductor': 4410, 'elladic_image': '3.4.0.1', 'lmfdb_label': '4410.bi8', 'modell_image': '3B', 'prime': 3}
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ec_padic • Show schema
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id: 157256
{'lmfdb_iso': '4410.bi', 'p': 13, 'prec': 20, 'unit': 750803199687706951901, 'val': 1}
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id: 157258
{'lmfdb_iso': '4410.bi', 'p': 17, 'prec': 20, 'unit': 154708475673715790787273, 'val': 1}
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id: 157248
{'lmfdb_iso': '4410.bi', 'p': 19, 'prec': 20, 'unit': 1896903539239952523362808, 'val': 1}
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id: 157255
{'lmfdb_iso': '4410.bi', 'p': 29, 'prec': 20, 'unit': 449400770143479020939998434, 'val': 1}
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id: 157265
{'lmfdb_iso': '4410.bi', 'p': 31, 'prec': 20, 'unit': 8752871050010787168570359319, 'val': 1}
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id: 157251
{'lmfdb_iso': '4410.bi', 'p': 37, 'prec': 20, 'unit': 245267122088056400266634069463, 'val': 1}
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id: 157253
{'lmfdb_iso': '4410.bi', 'p': 41, 'prec': 20, 'unit': 2221338963994005474379661049628, 'val': 1}
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id: 157254
{'lmfdb_iso': '4410.bi', 'p': 43, 'prec': 20, 'unit': 6571869624474957152488847784113, 'val': 1}
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id: 157260
{'lmfdb_iso': '4410.bi', 'p': 53, 'prec': 20, 'unit': 103172601269008802492261732356652, 'val': 1}
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id: 157263
{'lmfdb_iso': '4410.bi', 'p': 59, 'prec': 20, 'unit': 77574293523895889441093412102545, 'val': 1}
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id: 157264
{'lmfdb_iso': '4410.bi', 'p': 61, 'prec': 20, 'unit': 2173862210708834969173755377815581, 'val': 1}
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id: 157250
{'lmfdb_iso': '4410.bi', 'p': 67, 'prec': 20, 'unit': 24407743840574097998734715985495900, 'val': 1}
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id: 157252
{'lmfdb_iso': '4410.bi', 'p': 71, 'prec': 20, 'unit': 33798206520127427317226128928866786, 'val': 1}
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id: 157261
{'lmfdb_iso': '4410.bi', 'p': 73, 'prec': 20, 'unit': 4282676760686883391388116639276336, 'val': 1}
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id: 157257
{'lmfdb_iso': '4410.bi', 'p': 79, 'prec': 20, 'unit': 1064571551927719644392038105273444190, 'val': 1}
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id: 157259
{'lmfdb_iso': '4410.bi', 'p': 83, 'prec': 20, 'unit': 1797228756375593569152988608879184222, 'val': 1}
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id: 157262
{'lmfdb_iso': '4410.bi', 'p': 89, 'prec': 20, 'unit': 6531959434883240779797319584506021720, 'val': 1}
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id: 157249
{'lmfdb_iso': '4410.bi', 'p': 97, 'prec': 20, 'unit': 17724941938159461552770986160773910202, 'val': 1}