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ec_curvedata • Show schema
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{'Ciso': '14157l', 'Clabel': '14157l4', 'Cnumber': 4, 'abc_quality': 0.9895637859915349, 'absD': 1662119276103, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 6864, 'ainvs': [1, -1, 1, -7474919, 7867939016], 'analytic_rank': 1, 'bad_primes': [3, 11, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 14157, 'degree': 245760, 'elladic_images': ['8.24.0.87'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.2893494196401549390983520227', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 5, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [35765103905346817, 1287], 'lmfdb_iso': '14157.f', 'lmfdb_label': '14157.f1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -6864, 218313], 'min_quad_twist_disc': 33, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.24.0-8.n.1.1', '48.48.0-48.g.1.5', '132.12.0.?', '156.12.0.?', '176.48.0.?', '208.48.0.?', '264.48.0.?', '312.48.0.?', '528.96.0.?', '572.12.0.?', '624.96.0.?', '1144.48.0.?', '1716.24.0.?', '2288.96.0.?', '3432.96.0.?', '6864.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '7.5372177554209480305321898210', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.54109563890691482136975761526', 'prec': 103}, 'szpiro_ratio': 6.182780292990888, '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, 2, 0, 0, 3, 0, -2, 0, 0, -1, 0, 0, -1, -6, 0, 4, -2], 'aplist': [-1, 0, 2, 0, 0, -1, -6, 4, 8, -10, 0, 6, 10, -4, -8, 10, 12, -14, -12, 0, 6, -8, 12, -2, -14], 'class_deg': 8, 'class_size': 6, 'conductor': 14157, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '14157.f', 'trace_hash': 2124057353352221080}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.010268248249283949339780066959', 'prec': 107}, 'conductor': 14157, 'gens': [[68935, 4963417, 6]], 'heights': [{'__RealLiteral__': 0, 'data': '7.5372177554209480305321898210', 'prec': 100}], 'lmfdb_label': '14157.f1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.44984035645657530292334222503', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.3905447217893876717926120355033380605', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[6315, -6319, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [3, 0], '3': 'a', '5': [1, 0], '7': [3, 3, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '14157.f1'}
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ec_torsion_growth • Show schema
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id: 727912
{'degree': 2, 'field': [-143, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 2]}
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id: 727914
{'degree': 2, 'field': [-39, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [4]}
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id: 727913
{'degree': 2, 'field': [-8, -1, 1], 'lmfdb_label': '14157.f1', 'torsion': [8]}
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id: 727915
{'degree': 4, 'field': [676, 0, -91, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 8]}
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id: 727919
{'degree': 8, 'field': [27, 195, -87, 1071, 279, 108, 36, -1, 1], 'lmfdb_label': '14157.f1', 'torsion': [6]}
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id: 727916
{'degree': 8, 'field': [1459162, -153292, 151318, 3908, -1853, -124, 46, -4, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 4]}
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id: 727918
{'degree': 8, 'field': [1656369, 0, -169884, 0, 6897, 0, -132, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [16]}
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id: 727917
{'degree': 8, 'field': [49098049, 0, 0, 0, -4862, 0, 0, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [8]}
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id: 727924
{'degree': 16, 'field': [62001, -372753, 60102, 783807, -4233, 64242, 105628, -211733, 65973, -33537, 10128, -4503, 897, -108, 3, -2, 1], 'lmfdb_label': '14157.f1', 'torsion': [24]}
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id: 727925
{'degree': 16, 'field': [2313441, 0, -388763544, 0, 41876848, 0, 848211, 0, 139932, 0, -52351, 0, 2769, 0, -78, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [12]}
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id: 727923
{'degree': 16, 'field': [187388721, 0, 35195940, 0, -14458626, 0, -5001048, 0, 1704027, 0, -174759, 0, 7488, 0, -143, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 6]}
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id: 727922
{'degree': 16, 'field': [2998219536, 0, -6995845584, 0, 4589155116, 0, -844939836, 0, 63062181, 0, -2178072, 0, 37479, 0, -312, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 16]}
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id: 727921
{'degree': 16, 'field': [11322593649, 2483369910, -4298522598, -929137356, 776399745, 149022930, -83929158, -13946298, 6145840, 850504, -313696, -36374, 11605, 656, -184, -4, 1], 'lmfdb_label': '14157.f1', 'torsion': [2, 16]}
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id: 727920
{'degree': 16, 'field': [103247827684, 0, 23138557736, 0, -3584305840, 0, 119505156, 0, 35228549, 0, 23508, 0, -11698, 0, 8, 0, 1], 'lmfdb_label': '14157.f1', 'torsion': [4, 8]}
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ec_localdata • Show schema
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id: 310374
{'conductor': 14157, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '14157.f1', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 310375
{'conductor': 14157, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '14157.f1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 310376
{'conductor': 14157, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '14157.f1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1758104
{'adelic_gens': [[1, 16, 1724, 1845], [4298, 5159, 2491, 3318], [6849, 16, 6848, 17], [1, 16, 0, 1], [2275, 6848, 4832, 315], [15, 2, 6766, 6851], [5, 4, 6860, 6861], [536, 1, 2719, 10], [1, 0, 16, 1], [5600, 6859, 4413, 14]], 'adelic_image': '6864.192.1.?', 'conductor': 14157, 'lmfdb_label': '14157.f1', 'prime': 0}
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id: 66984
{'conductor': 14157, 'elladic_image': '8.24.0.87', 'lmfdb_label': '14157.f1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 631094
{'lmfdb_iso': '14157.f', 'p': 5, 'prec': 20, 'unit': 11514931422968, 'val': 1}
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id: 631085
{'lmfdb_iso': '14157.f', 'p': 17, 'prec': 20, 'unit': 219681782003920711361801, 'val': 1}
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id: 631077
{'lmfdb_iso': '14157.f', 'p': 19, 'prec': 20, 'unit': 1726719152801131434424475, 'val': 1}
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id: 631090
{'lmfdb_iso': '14157.f', 'p': 23, 'prec': 20, 'unit': 52701965330095192605508903, 'val': 1}
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id: 631083
{'lmfdb_iso': '14157.f', 'p': 29, 'prec': 20, 'unit': 3279265076572823363513335761, 'val': 1}
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id: 631080
{'lmfdb_iso': '14157.f', 'p': 37, 'prec': 20, 'unit': 20494756213756464417145152820, 'val': 1}
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id: 631081
{'lmfdb_iso': '14157.f', 'p': 41, 'prec': 20, 'unit': 1312784203837786623181750049018, 'val': 1}
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id: 631082
{'lmfdb_iso': '14157.f', 'p': 43, 'prec': 20, 'unit': 3820247131679554997801993343790, 'val': 1}
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id: 631092
{'lmfdb_iso': '14157.f', 'p': 47, 'prec': 20, 'unit': 53390606917819744352701558661263, 'val': 1}
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id: 631087
{'lmfdb_iso': '14157.f', 'p': 53, 'prec': 20, 'unit': 295335203649084434031423832358672, 'val': 1}
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id: 631088
{'lmfdb_iso': '14157.f', 'p': 59, 'prec': 20, 'unit': 1766277486110866590498473672071963, 'val': 1}
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id: 631093
{'lmfdb_iso': '14157.f', 'p': 61, 'prec': 20, 'unit': 6560709275685646494059276203137638, 'val': 1}
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id: 631079
{'lmfdb_iso': '14157.f', 'p': 67, 'prec': 20, 'unit': 5218564117498896253870919054917516, 'val': 1}
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id: 631089
{'lmfdb_iso': '14157.f', 'p': 73, 'prec': 20, 'unit': 90810289860033203942123455073667995, 'val': 1}
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id: 631084
{'lmfdb_iso': '14157.f', 'p': 79, 'prec': 20, 'unit': 690071570787247852408970457519239528, 'val': 1}
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id: 631086
{'lmfdb_iso': '14157.f', 'p': 83, 'prec': 20, 'unit': 1093258262511741070274640072925617795, 'val': 1}
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id: 631091
{'lmfdb_iso': '14157.f', 'p': 89, 'prec': 20, 'unit': 9233265925012852046966053150126390650, 'val': 1}
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id: 631078
{'lmfdb_iso': '14157.f', 'p': 97, 'prec': 20, 'unit': 53189224909884470366734409738099552352, 'val': 1}