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ec_curvedata • Show schema
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{'Ciso': '38720bs', 'Clabel': '38720bs2', 'Cnumber': 2, 'abc_quality': 1.0555982735754514, 'absD': 1404822362521600, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 440, 'ainvs': [0, 0, 0, -32428, 1341648], 'analytic_rank': 1, 'bad_primes': [2, 5, 11], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 38720, 'degree': 122880, 'elladic_images': ['8.12.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.6064293369843716807852165008', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 43, 'isogeny_degrees': [1, 2], 'jinv': [8120601, 3025], 'lmfdb_iso': '38720.br', 'lmfdb_label': '38720.br3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -4, 3], 'min_quad_twist_disc': 88, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '8.12.0-2.a.1.1', '20.12.0.b.1', '40.24.0-20.b.1.4', '44.12.0.a.1', '88.24.0.?', '220.24.0.?', '440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '5.4224859628990910354854610891', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.63223907025473155537160347037', 'prec': 107}, 'szpiro_ratio': 4.048985609765372, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, -1, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, -6, 0, 4, 0], 'aplist': [0, 0, -1, 0, 0, 2, -6, 4, -4, 6, 8, 2, -2, -4, 12, 2, 4, -10, -16, -8, -14, 8, 4, 10, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 38720, 'isogeny_matrix': [[1, 4, 2, 4], [4, 1, 2, 4], [2, 2, 1, 2], [4, 4, 2, 1]], 'lmfdb_iso': '38720.br', 'trace_hash': 280321634549290917}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.040241411612648647256854400326', 'prec': 107}, 'conductor': 38720, 'gens': [[-182, 38080, 3]], 'heights': [{'__RealLiteral__': 0, 'data': '5.4224859628990910354854610891', 'prec': 100}], 'lmfdb_label': '38720.br3', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.43862630046122534156442378366', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.7568899144187070292491663135095158697', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[44, 0, 1], [154, 0, 1]], 'xcoord_integral_points': [-198, 44, 154]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 1, 0], '5': [1, 0], '7': [1, 1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '38720.br3'}
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ec_torsion_growth • Show schema
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id: 1909215
{'degree': 4, 'field': [25, 0, 12, 0, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 4]}
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id: 1909214
{'degree': 4, 'field': [254, -24, 25, -2, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 4]}
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id: 1909213
{'degree': 4, 'field': [419, 46, -45, -2, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 4]}
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id: 1909216
{'degree': 8, 'field': [-5808, 0, 2376, 0, -264, 0, 0, 0, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 6]}
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id: 1909218
{'degree': 16, 'field': [-30164, -178040, -279468, -195320, 16160, 150620, 99362, 23960, 7659, 4040, -442, -440, 120, -20, -32, 0, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 8]}
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id: 1909220
{'degree': 16, 'field': [1369, 0, 2576, 0, 9326, 0, 7864, 0, 2947, 0, 424, 0, 38, 0, 8, 0, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 8]}
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id: 1909217
{'degree': 16, 'field': [14436, -9048, 12652, -11256, 19586, -28952, 34622, -31532, 22557, -13112, 6314, -2492, 840, -224, 52, -8, 1], 'lmfdb_label': '38720.br3', 'torsion': [4, 4]}
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id: 1909219
{'degree': 16, 'field': [1893376, 0, 368256, 0, -268400, 0, -1376, 0, 14824, 0, -3136, 0, 385, 0, -24, 0, 1], 'lmfdb_label': '38720.br3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 914171
{'conductor': 38720, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '38720.br3', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 914172
{'conductor': 38720, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '38720.br3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 914173
{'conductor': 38720, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '38720.br3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1922308
{'adelic_gens': [[223, 436, 224, 435], [101, 2, 0, 1], [1, 4, 0, 1], [437, 4, 436, 5], [1, 0, 4, 1], [113, 4, 8, 11], [349, 438, 354, 221], [219, 0, 0, 439]], 'adelic_image': '440.48.0.?', 'conductor': 38720, 'lmfdb_label': '38720.br3', 'prime': 0}
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id: 170297
{'conductor': 38720, 'elladic_image': '8.12.0.1', 'lmfdb_label': '38720.br3', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 1910712
{'lmfdb_iso': '38720.br', 'p': 13, 'prec': 20, 'unit': 1297874380601878348894, 'val': 1}
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id: 1910714
{'lmfdb_iso': '38720.br', 'p': 17, 'prec': 20, 'unit': 74372567254549044864283, 'val': 1}
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id: 1910715
{'lmfdb_iso': '38720.br', 'p': 19, 'prec': 20, 'unit': 467166321881390914690134, 'val': 1}
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id: 1910719
{'lmfdb_iso': '38720.br', 'p': 23, 'prec': 20, 'unit': 67769979660439149233953453, 'val': 1}
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id: 1910711
{'lmfdb_iso': '38720.br', 'p': 29, 'prec': 20, 'unit': 3337202547686465405924663561, 'val': 1}
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id: 1910723
{'lmfdb_iso': '38720.br', 'p': 31, 'prec': 20, 'unit': 12357256818701241686039659698, 'val': 1}
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id: 1910707
{'lmfdb_iso': '38720.br', 'p': 37, 'prec': 20, 'unit': 511329789094028780334938778572, 'val': 1}
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id: 1910709
{'lmfdb_iso': '38720.br', 'p': 41, 'prec': 20, 'unit': 1030725975528535515217668754169, 'val': 1}
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id: 1910710
{'lmfdb_iso': '38720.br', 'p': 43, 'prec': 20, 'unit': 3311767944714326902654071103497, 'val': 1}
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id: 1910721
{'lmfdb_iso': '38720.br', 'p': 47, 'prec': 20, 'unit': 21418794155668837259902756288195, 'val': 1}
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id: 1910716
{'lmfdb_iso': '38720.br', 'p': 53, 'prec': 20, 'unit': 216212910950655157783020933493135, 'val': 1}
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id: 1910717
{'lmfdb_iso': '38720.br', 'p': 59, 'prec': 20, 'unit': 40523365670054001479762643134517, 'val': 1}
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id: 1910722
{'lmfdb_iso': '38720.br', 'p': 61, 'prec': 20, 'unit': 2329887179027523205914676309195288, 'val': 1}
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id: 1910706
{'lmfdb_iso': '38720.br', 'p': 67, 'prec': 20, 'unit': 7021208819992133672256974980023285, 'val': 1}
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id: 1910708
{'lmfdb_iso': '38720.br', 'p': 71, 'prec': 20, 'unit': 36938477648393024730202267346874963, 'val': 1}
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id: 1910718
{'lmfdb_iso': '38720.br', 'p': 73, 'prec': 20, 'unit': 247789927869812966708636350127754177, 'val': 1}
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id: 1910713
{'lmfdb_iso': '38720.br', 'p': 79, 'prec': 20, 'unit': 1097917331490898782440110688818562612, 'val': 1}
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id: 1910705
{'lmfdb_iso': '38720.br', 'p': 83, 'prec': 20, 'unit': 1783450283338935680680383063536218228, 'val': 1}
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id: 1910720
{'lmfdb_iso': '38720.br', 'p': 89, 'prec': 20, 'unit': 4989584277505752406559207554027400381, 'val': 1}
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id: 1910704
{'lmfdb_iso': '38720.br', 'p': 97, 'prec': 20, 'unit': 31982570128479850633679354544243904072, 'val': 1}