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ec_curvedata • Show schema
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{'Ciso': '47040cn', 'Clabel': '47040cn4', 'Cnumber': 4, 'abc_quality': 1.0397263843855777, 'absD': 40659494400000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 168, 'ainvs': [0, 1, 0, -97281, -6534081], 'analytic_rank': 1, 'bad_primes': [2, 3, 5, 7], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 47040, 'degree': 442368, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.8851691050252932161382571801', 'prec': 100}, 'faltings_index': 2, 'faltings_ratio': 4, 'iso_nlabel': 140, 'isogeny_degrees': [1, 2, 4], 'jinv': [26410345352, 10546875], 'lmfdb_iso': '47040.fk', 'lmfdb_label': '47040.fk1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -496, -2204], 'min_quad_twist_disc': 56, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '24.24.0.bi.1', '28.12.0-4.c.1.2', '56.24.0-8.m.1.3', '168.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '2.2931034717909357498336233515', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.045780054797704926814040656555', 'prec': 107}, 'szpiro_ratio': 4.282065751286337, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 4, 0, 6, 0, -1, 0, -2, 0, -4, 0], 'aplist': [0, 1, -1, 0, 4, 6, -2, -4, 0, -10, -4, 10, -2, -4, 8, -2, -12, -10, 12, 0, -10, 4, -4, 6, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 47040, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '47040.fk', 'trace_hash': 1646365695419848459}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.023044268166003551840714460986', 'prec': 107}, 'conductor': 47040, 'gens': [[-75, 588, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '2.2931034717909357498336233515', 'prec': 100}], 'lmfdb_label': '47040.fk1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.27981641978147729054296303738', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '7.6997760439801853549684000932647439160', 'prec': 130}, 'tamagawa_product': 48, 'torsion_generators': [[-271, 0, 1]], 'xcoord_integral_points': [-271, -75, 354]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [6, 0], '5': [1, 0], '7': 'a', '11': [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, 0]}, 'iwp0': 0, 'lmfdb_label': '47040.fk1'}
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ec_torsion_growth • Show schema
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id: 2293808
{'degree': 2, 'field': [-6, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 2]}
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id: 2293809
{'degree': 2, 'field': [2, -1, 1], 'lmfdb_label': '47040.fk1', 'torsion': [4]}
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id: 2293810
{'degree': 2, 'field': [42, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [4]}
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id: 2293811
{'degree': 4, 'field': [58, 8, -7, -2, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 4]}
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id: 2293815
{'degree': 8, 'field': [-24555, 42972, -30922, 10044, -816, -288, 30, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [6]}
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id: 2293813
{'degree': 8, 'field': [2, -8, 80, -160, 121, -52, 22, -4, 1], 'lmfdb_label': '47040.fk1', 'torsion': [8]}
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id: 2293812
{'degree': 8, 'field': [81, 0, -108, 0, -240, 0, -12, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 4]}
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id: 2293814
{'degree': 8, 'field': [1086, -840, 636, -192, 70, -16, 12, -4, 1], 'lmfdb_label': '47040.fk1', 'torsion': [8]}
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id: 2293819
{'degree': 16, 'field': [-110295, -198396, 96048, -78228, 118638, -37656, 15732, -18972, -336, 5484, 984, -1932, 270, 144, -32, -4, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 6]}
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id: 2293817
{'degree': 16, 'field': [4, -16, -96, 0, 4878, -10968, 15592, -11224, 4623, 420, -438, -336, 155, 16, -6, -4, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 8]}
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id: 2293816
{'degree': 16, 'field': [2116, 0, 8016, 0, 20572, 0, -3888, 0, 3045, 0, -324, 0, 46, 0, -12, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [4, 4]}
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id: 2293820
{'degree': 16, 'field': [3028, 9344, 27080, -124608, 200996, -192896, 109792, -41904, 14485, -3384, 1636, -856, 446, -168, 44, -8, 1], 'lmfdb_label': '47040.fk1', 'torsion': [12]}
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id: 2293818
{'degree': 16, 'field': [33678, 29232, 45972, 27720, 26526, 10848, 8004, 2244, 1279, 36, 232, 132, 66, -12, -8, 0, 1], 'lmfdb_label': '47040.fk1', 'torsion': [2, 8]}
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id: 2293821
{'degree': 16, 'field': [8195041, -11840768, 3687752, 3795548, 278194, -912348, -273728, 74620, 53792, -1240, -2984, -684, 370, 4, -4, -4, 1], 'lmfdb_label': '47040.fk1', 'torsion': [12]}
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ec_localdata • Show schema
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id: 1122402
{'conductor': 47040, 'conductor_valuation': 6, 'discriminant_valuation': 15, 'j_denominator_valuation': 0, 'kodaira_symbol': -9, 'lmfdb_label': '47040.fk1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 1122403
{'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '47040.fk1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 3}
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id: 1122404
{'conductor': 47040, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '47040.fk1', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1122405
{'conductor': 47040, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '47040.fk1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1977590
{'adelic_gens': [[48, 7, 119, 132], [1, 0, 8, 1], [1, 8, 0, 1], [64, 147, 133, 50], [48, 7, 77, 90], [7, 6, 162, 163], [161, 8, 160, 9], [95, 0, 0, 167], [1, 4, 4, 17]], 'adelic_image': '168.48.0.?', 'conductor': 47040, 'lmfdb_label': '47040.fk1', 'prime': 0}
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id: 203528
{'conductor': 47040, 'elladic_image': '8.12.0.11', 'lmfdb_label': '47040.fk1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 2358644
{'lmfdb_iso': '47040.fk', 'p': 11, 'prec': 20, 'unit': 53230619524752286744, 'val': 1}
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id: 2358649
{'lmfdb_iso': '47040.fk', 'p': 13, 'prec': 20, 'unit': 1331964092632105809739, 'val': 1}
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id: 2358651
{'lmfdb_iso': '47040.fk', 'p': 17, 'prec': 20, 'unit': 18839172026040252491401, 'val': 1}
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id: 2358652
{'lmfdb_iso': '47040.fk', 'p': 19, 'prec': 20, 'unit': 1303902604076566527843950, 'val': 1}
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id: 2358648
{'lmfdb_iso': '47040.fk', 'p': 29, 'prec': 20, 'unit': 5135660180818123506958283558, 'val': 1}
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id: 2358660
{'lmfdb_iso': '47040.fk', 'p': 31, 'prec': 20, 'unit': 2036577908145443281059763816, 'val': 1}
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id: 2358645
{'lmfdb_iso': '47040.fk', 'p': 37, 'prec': 20, 'unit': 320469615363349569974018903461, 'val': 1}
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id: 2358646
{'lmfdb_iso': '47040.fk', 'p': 41, 'prec': 20, 'unit': 92158222235242731611171461601, 'val': 1}
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id: 2358647
{'lmfdb_iso': '47040.fk', 'p': 43, 'prec': 20, 'unit': 6816920607989974117176667912507, 'val': 1}
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id: 2358658
{'lmfdb_iso': '47040.fk', 'p': 47, 'prec': 20, 'unit': 57058018245018015896817218157979, 'val': 1}
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id: 2358653
{'lmfdb_iso': '47040.fk', 'p': 53, 'prec': 20, 'unit': 193807001559679768828518604306877, 'val': 1}
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id: 2358654
{'lmfdb_iso': '47040.fk', 'p': 59, 'prec': 20, 'unit': 3892902327598021416667917403281707, 'val': 1}
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id: 2358659
{'lmfdb_iso': '47040.fk', 'p': 61, 'prec': 20, 'unit': 2388296408898608450272981568009641, 'val': 1}
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id: 2358643
{'lmfdb_iso': '47040.fk', 'p': 67, 'prec': 20, 'unit': 4942410504123466989708479785008343, 'val': 1}
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id: 2358655
{'lmfdb_iso': '47040.fk', 'p': 73, 'prec': 20, 'unit': 177191014557492951926229010293919362, 'val': 1}
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id: 2358650
{'lmfdb_iso': '47040.fk', 'p': 79, 'prec': 20, 'unit': 1106707299358106495728125543424521934, 'val': 1}
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id: 2358656
{'lmfdb_iso': '47040.fk', 'p': 83, 'prec': 20, 'unit': 1893385017752664721828964613603519804, 'val': 1}
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id: 2358657
{'lmfdb_iso': '47040.fk', 'p': 89, 'prec': 20, 'unit': 951509957171018316153155195881855547, 'val': 1}
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id: 2358642
{'lmfdb_iso': '47040.fk', 'p': 97, 'prec': 20, 'unit': 30817486421563957168304187950944145612, 'val': 1}