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ec_curvedata • Show schema
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{'Ciso': '1656f', 'Clabel': '1656f1', 'Cnumber': 1, 'abc_quality': 0.9038338202074565, 'absD': 17169408, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 184, 'ainvs': [0, 0, 0, 45, -162], 'analytic_rank': 1, 'bad_primes': [2, 3, 23], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 1656, 'degree': 384, 'elladic_images': ['8.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.073185217854674144719281611729', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [13500, 23], 'lmfdb_iso': '1656.e', 'lmfdb_label': '1656.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 0, 0, 5, 6], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '8.6.0.c.1', '46.6.0.a.1', '184.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 7, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2920311278156061527675258083', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.0537435769460017921593677746', 'prec': 103}, 'szpiro_ratio': 3.1972241744886745, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, 0, -2, 0, 0, 0, -6, 0, -6, 0], 'aplist': [0, 0, 0, 4, -6, -2, -6, -6, -1, 6, 0, -8, -6, -2, 8, 8, -4, -4, 2, 8, 6, 12, -10, -10, -18], 'class_deg': 2, 'class_size': 2, 'conductor': 1656, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '1656.e', 'trace_hash': 717446676828261975}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.86383764759654407326882329349', 'prec': 103}, 'conductor': 1656, 'gens': [[6, 18, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2920311278156061527675258083', 'prec': 100}], 'lmfdb_label': '1656.e2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.1518396659643191050647289356', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9764254053572605473332069597964361655', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[3, 0, 1]], 'xcoord_integral_points': [3, 6, 27, 336678]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': 'a', '5': [1, 5, 0], '7': [1, 0], '11': [3, 0], '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': '1656.e2'}
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ec_torsion_growth • Show schema
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id: 82974
{'degree': 2, 'field': [6, -1, 1], 'lmfdb_label': '1656.e2', 'torsion': [2, 2]}
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id: 82975
{'degree': 4, 'field': [-14, 4, -3, -2, 1], 'lmfdb_label': '1656.e2', 'torsion': [4]}
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id: 82978
{'degree': 8, 'field': [-12, -48, -84, -84, -60, -36, -12, 0, 1], 'lmfdb_label': '1656.e2', 'torsion': [6]}
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id: 82977
{'degree': 8, 'field': [82, -100, 361, -130, 57, -8, -5, -2, 1], 'lmfdb_label': '1656.e2', 'torsion': [2, 4]}
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id: 82976
{'degree': 8, 'field': [468, -396, 432, -282, 211, -68, 12, -2, 1], 'lmfdb_label': '1656.e2', 'torsion': [2, 4]}
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id: 82979
{'degree': 16, 'field': [4, 0, 4336, 0, -4552, 0, 3280, 0, -992, 0, 8, 0, 44, 0, -16, 0, 1], 'lmfdb_label': '1656.e2', 'torsion': [8]}
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id: 82980
{'degree': 16, 'field': [8100, 0, 26568, 0, -33804, 0, 18252, 0, -4212, 0, 792, 0, -48, 0, 0, 0, 1], 'lmfdb_label': '1656.e2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 26024
{'conductor': 1656, 'conductor_valuation': 3, 'discriminant_valuation': 10, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '1656.e2', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 26025
{'conductor': 1656, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '1656.e2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 26026
{'conductor': 1656, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '1656.e2', 'prime': 23, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1674827
{'adelic_gens': [[1, 2, 2, 5], [25, 162, 160, 23], [10, 1, 87, 0], [3, 4, 8, 11], [93, 4, 2, 9], [181, 4, 180, 5], [1, 4, 0, 1], [1, 0, 4, 1]], 'adelic_image': '184.12.0.?', 'conductor': 1656, 'lmfdb_label': '1656.e2', 'prime': 0}
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id: 8037
{'conductor': 1656, 'elladic_image': '8.6.0.1', 'lmfdb_label': '1656.e2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 44984
{'lmfdb_iso': '1656.e', 'p': 7, 'prec': 20, 'unit': 6044077717373242, 'val': 1}
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id: 44982
{'lmfdb_iso': '1656.e', 'p': 11, 'prec': 20, 'unit': 3928745010920750514, 'val': 2}
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id: 44988
{'lmfdb_iso': '1656.e', 'p': 13, 'prec': 20, 'unit': 1240526876379418276258, 'val': 1}
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id: 44990
{'lmfdb_iso': '1656.e', 'p': 17, 'prec': 20, 'unit': 75199590041106335219785, 'val': 1}
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id: 44991
{'lmfdb_iso': '1656.e', 'p': 19, 'prec': 20, 'unit': 1513986410851621677416358, 'val': 1}
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id: 44987
{'lmfdb_iso': '1656.e', 'p': 29, 'prec': 20, 'unit': 653519489374395163930148038, 'val': 1}
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id: 44983
{'lmfdb_iso': '1656.e', 'p': 37, 'prec': 20, 'unit': 111493807092751111556973543190, 'val': 1}
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id: 44985
{'lmfdb_iso': '1656.e', 'p': 41, 'prec': 20, 'unit': 814070001917105240653350375358, 'val': 1}
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id: 44986
{'lmfdb_iso': '1656.e', 'p': 43, 'prec': 20, 'unit': 2223745533915214319001324013210, 'val': 1}
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id: 44998
{'lmfdb_iso': '1656.e', 'p': 47, 'prec': 20, 'unit': 19028766426241848953920672536485, 'val': 1}
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id: 44992
{'lmfdb_iso': '1656.e', 'p': 53, 'prec': 20, 'unit': 227294847737765208409372749501885, 'val': 1}
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id: 44993
{'lmfdb_iso': '1656.e', 'p': 59, 'prec': 20, 'unit': 1211291510064687713910213884559741, 'val': 1}
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id: 44999
{'lmfdb_iso': '1656.e', 'p': 61, 'prec': 20, 'unit': 6528474293172217632210324901869800, 'val': 1}
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id: 44981
{'lmfdb_iso': '1656.e', 'p': 67, 'prec': 20, 'unit': 40412155885332756896386211956053237, 'val': 1}
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id: 44997
{'lmfdb_iso': '1656.e', 'p': 71, 'prec': 20, 'unit': 23198834739088528095273721457069225, 'val': 1}
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id: 44994
{'lmfdb_iso': '1656.e', 'p': 73, 'prec': 20, 'unit': 72315670210031658894941650865176804, 'val': 1}
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id: 44989
{'lmfdb_iso': '1656.e', 'p': 79, 'prec': 20, 'unit': 83606498967167323908693785940616447, 'val': 1}
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id: 44995
{'lmfdb_iso': '1656.e', 'p': 83, 'prec': 20, 'unit': 1828600708741844755261404717547388882, 'val': 1}
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id: 44996
{'lmfdb_iso': '1656.e', 'p': 89, 'prec': 20, 'unit': 5522707852423850814188086161992947368, 'val': 1}
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id: 44980
{'lmfdb_iso': '1656.e', 'p': 97, 'prec': 20, 'unit': 22644098187944430963707179566591837503, 'val': 1}