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ec_curvedata • Show schema
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{'Ciso': '51870k', 'Clabel': '51870k1', 'Cnumber': 1, 'abc_quality': 1.0122284725612463, 'absD': 7250093712589769932800, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 3192, 'ainvs': [1, 1, 0, -305859437, -2059002924771], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 7, 13, 19], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 51870, 'degree': 13381632, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '3.4383063003947973994458097700', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 14, 'isogeny_degrees': [1, 2], 'jinv': [3164385375313381150271070759001, 7250093712589769932800], 'lmfdb_iso': '51870.o', 'lmfdb_label': '51870.o1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -305859437, -2059002924771], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '56.6.0.c.1', '114.6.0.?', '3192.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 6, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '3.4383063003947973994458097700', 'prec': 100}, 'szpiro_ratio': 6.468893139229612, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, 1, 1, -1, -1, 1, -1, -2, -1, -1, 1, -1, 1, 4, -1, -1, 1], 'aplist': [-1, -1, 1, -1, -2, -1, 4, -1, -4, -10, -2, -12, -2, -8, 6, -6, -12, -2, -2, 0, 6, 4, -12, -10, -8], 'class_deg': 2, 'class_size': 2, 'conductor': 51870, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '51870.o', 'trace_hash': 1692360159519509646}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0010316326848733596882028585482', 'prec': 110}, 'conductor': 51870, 'gens': [], 'heights': [], 'lmfdb_label': '51870.o1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.036100992597100553471569094715', 'prec': 107}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.14440397038840221388627637886143302992', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[-10086, 5043, 1]], 'xcoord_integral_points': [-10086]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [8, 0], '3': [0, 0], '5': [1, 0], '7': [0, 0], '13': [0, 0], '19': [0, 0]}, 'iwp0': 3, 'lmfdb_label': '51870.o1'}
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ec_torsion_growth • Show schema
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id: 2510512
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '51870.o1', 'torsion': [2, 2]}
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id: 2510513
{'degree': 4, 'field': [9, 6, 9, -2, 1], 'lmfdb_label': '51870.o1', 'torsion': [4]}
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id: 2510516
{'degree': 8, 'field': [-243, 0, -612, 0, 54, 0, 0, 0, 1], 'lmfdb_label': '51870.o1', 'torsion': [6]}
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id: 2510515
{'degree': 8, 'field': [4713, 3888, 3358, 860, -85, 20, 26, -4, 1], 'lmfdb_label': '51870.o1', 'torsion': [2, 4]}
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id: 2510514
{'degree': 8, 'field': [178654, -269822, 115057, -1448, -7196, 610, 22, -2, 1], 'lmfdb_label': '51870.o1', 'torsion': [2, 4]}
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id: 2510518
{'degree': 16, 'field': [1492883584, 1456754584, -1265484468, -363629968, 136633724, 48504840, -7096508, -6894584, 661077, 648664, -71600, -29712, 3314, 728, -84, -8, 1], 'lmfdb_label': '51870.o1', 'torsion': [2, 6]}
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id: 2510517
{'degree': 16, 'field': [14685446577, -4023810792, 2497148392, -532468104, 857429050, -152927904, 73652620, -17369968, 7731823, -1377648, 393260, -58928, 12850, -1064, 204, -8, 1], 'lmfdb_label': '51870.o1', 'torsion': [8]}
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ec_localdata • Show schema
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id: 1241023
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 22, 'j_denominator_valuation': 22, 'kodaira_symbol': 26, 'lmfdb_label': '51870.o1', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241024
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '51870.o1', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 1241025
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '51870.o1', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 1241026
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '51870.o1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241027
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '51870.o1', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 1241028
{'conductor': 51870, 'conductor_valuation': 1, 'discriminant_valuation': 3, 'j_denominator_valuation': 3, 'kodaira_symbol': 7, 'lmfdb_label': '51870.o1', 'prime': 19, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 2008826
{'adelic_gens': [[1597, 4, 2, 9], [401, 2794, 2792, 399], [1, 2, 2, 5], [1, 4, 0, 1], [1066, 1, 1063, 0], [3189, 4, 3188, 5], [2018, 1, 2183, 0], [1, 0, 4, 1], [3, 4, 8, 11], [913, 4, 1826, 9]], 'adelic_image': '3192.12.0.?', 'conductor': 51870, 'lmfdb_label': '51870.o1', 'prime': 0}
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id: 222018
{'conductor': 51870, 'elladic_image': '2.3.0.1', 'lmfdb_label': '51870.o1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 51870.o does not appear in ec_padic
