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ec_curvedata • Show schema
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{'Ciso': '21175bb', 'Clabel': '21175bb1', 'Cnumber': 1, 'abc_quality': 0.9828796710470877, 'absD': 91384174943359375, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 220, 'ainvs': [1, 0, 1, -243576, 48481673], 'analytic_rank': 1, 'bad_primes': [5, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 21175, 'degree': 249600, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0112500824466587728499538261', 'prec': 100}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 25, 'isogeny_degrees': [1, 2], 'jinv': [-461889917, 26411], 'lmfdb_iso': '21175.z', 'lmfdb_label': '21175.z2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 0, -80, -325], 'min_quad_twist_disc': -55, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '20.6.0.c.1', '44.6.0.d.1', '110.6.0.?', '220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '3.8554936260181865758781711383', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.39477598827810178013158746280', 'prec': 107}, 'szpiro_ratio': 4.911098814300066, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, -2, -1, 0, -2, -1, -3, 1, 0, 0, 2, -6, -1, 0, -1, -6, 1, 0, 0], 'aplist': [1, -2, 0, -1, 0, -6, -6, 0, -6, 6, 0, -4, 6, -8, 10, -4, 12, 10, 2, 8, 2, -8, 0, -6, 0], 'class_deg': 2, 'class_size': 2, 'conductor': 21175, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '21175.z', 'trace_hash': 2254181167066117621}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.017908135630514090538936528282', 'prec': 107}, 'conductor': 21175, 'gens': [[211, 2442, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '3.8554936260181865758781711383', 'prec': 100}], 'lmfdb_label': '21175.z2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.33443216000593656960794955614', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.5788021224767654842756069382394776433', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-573, 286, 1]], 'xcoord_integral_points': [-573, 211]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '3': [1, 0], '5': 'a', '7': [1, 0], '11': 'a', '13': [1, 0], '17': [1, 0], '19': [1, 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': '21175.z2'}
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ec_torsion_growth • Show schema
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id: 1078107
{'degree': 2, 'field': [14, -1, 1], 'lmfdb_label': '21175.z2', 'torsion': [2, 2]}
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id: 1078108
{'degree': 4, 'field': [-4, 4, 1, -1, 1], 'lmfdb_label': '21175.z2', 'torsion': [4]}
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id: 1078111
{'degree': 8, 'field': [-249, 849, -828, -43, 25, -7, 7, -4, 1], 'lmfdb_label': '21175.z2', 'torsion': [6]}
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id: 1078110
{'degree': 8, 'field': [1, 0, -1, 0, 16, 0, -1, 0, 1], 'lmfdb_label': '21175.z2', 'torsion': [2, 4]}
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id: 1078109
{'degree': 8, 'field': [3481, 0, -507, 0, 24, 0, -3, 0, 1], 'lmfdb_label': '21175.z2', 'torsion': [2, 4]}
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id: 1078112
{'degree': 16, 'field': [13916, 114464, -1023778, 1062754, 303893, -640696, 7381, 146652, -17707, -12906, 3014, -560, -47, 138, -17, -6, 1], 'lmfdb_label': '21175.z2', 'torsion': [8]}
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id: 1078113
{'degree': 16, 'field': [2369691, 9242334, 11234592, -10616469, -580047, -2177604, 1595258, -347764, 222904, -50190, 21055, -2648, 1082, -105, 35, -4, 1], 'lmfdb_label': '21175.z2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 481945
{'conductor': 21175, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '21175.z2', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 481946
{'conductor': 21175, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21175.z2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 481947
{'conductor': 21175, 'conductor_valuation': 2, 'discriminant_valuation': 7, 'j_denominator_valuation': 1, 'kodaira_symbol': -5, 'lmfdb_label': '21175.z2', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1805677
{'adelic_gens': [[57, 166, 164, 55], [1, 2, 2, 5], [202, 1, 119, 0], [217, 4, 216, 5], [3, 4, 8, 11], [1, 4, 0, 1], [48, 1, 43, 0], [1, 0, 4, 1]], 'adelic_image': '220.12.0.?', 'conductor': 21175, 'lmfdb_label': '21175.z2', 'prime': 0}
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id: 98247
{'conductor': 21175, 'elladic_image': '2.3.0.1', 'lmfdb_label': '21175.z2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 992433
{'lmfdb_iso': '21175.z', 'p': 13, 'prec': 20, 'unit': 110871343580914724111, 'val': 1}
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id: 992435
{'lmfdb_iso': '21175.z', 'p': 17, 'prec': 20, 'unit': 115904462573042612833651, 'val': 1}
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id: 992439
{'lmfdb_iso': '21175.z', 'p': 23, 'prec': 20, 'unit': 73375129059953302403219555, 'val': 1}
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id: 992432
{'lmfdb_iso': '21175.z', 'p': 29, 'prec': 20, 'unit': 20578238167558206007151908, 'val': 1}
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id: 992428
{'lmfdb_iso': '21175.z', 'p': 37, 'prec': 20, 'unit': 492584662660942648472866810437, 'val': 1}
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id: 992430
{'lmfdb_iso': '21175.z', 'p': 41, 'prec': 20, 'unit': 4351176670298177419438015064541, 'val': 1}
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id: 992431
{'lmfdb_iso': '21175.z', 'p': 43, 'prec': 20, 'unit': 9286851460943412004390737323630, 'val': 1}
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id: 992441
{'lmfdb_iso': '21175.z', 'p': 47, 'prec': 20, 'unit': 56460489637321681925835090969034, 'val': 1}
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id: 992436
{'lmfdb_iso': '21175.z', 'p': 53, 'prec': 20, 'unit': 256753206037970268398776164662479, 'val': 1}
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id: 992437
{'lmfdb_iso': '21175.z', 'p': 59, 'prec': 20, 'unit': 3800125465968326188334992900228569, 'val': 1}
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id: 992442
{'lmfdb_iso': '21175.z', 'p': 61, 'prec': 20, 'unit': 2927583364897931301517976106608596, 'val': 1}
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id: 992427
{'lmfdb_iso': '21175.z', 'p': 67, 'prec': 20, 'unit': 6641467493564281276697063534025398, 'val': 1}
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id: 992429
{'lmfdb_iso': '21175.z', 'p': 71, 'prec': 20, 'unit': 78378514020602301508372929725507495, 'val': 1}
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id: 992438
{'lmfdb_iso': '21175.z', 'p': 73, 'prec': 20, 'unit': 71219963053749394125067927978263037, 'val': 1}
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id: 992434
{'lmfdb_iso': '21175.z', 'p': 79, 'prec': 20, 'unit': 266900564728587353940702553922209528, 'val': 1}
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id: 992440
{'lmfdb_iso': '21175.z', 'p': 89, 'prec': 20, 'unit': 276199845900377710711830577289708930, 'val': 1}