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ec_curvedata • Show schema
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{'Ciso': '21175bc', 'Clabel': '21175bc2', 'Cnumber': 2, 'abc_quality': 0.9264268694934893, 'absD': 300357403240876953125, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 220, 'ainvs': [1, 1, 1, -3533263, -2417958344], 'analytic_rank': 1, 'bad_primes': [5, 7, 11], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 21175, 'degree': 806400, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.6810940395400869901256704172', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 12, 'isogeny_degrees': [1, 2], 'jinv': [1409825840597, 86806489], 'lmfdb_iso': '21175.m', 'lmfdb_label': '21175.m1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -1168, 14427], 'min_quad_twist_disc': -55, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '10.6.0.a.1', '44.6.0.d.1', '220.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '9.5352892346627978809462495994', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.27506796881532643714412912830', 'prec': 103}, 'szpiro_ratio': 5.707179703170209, '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, -2, 1, 0, -1, -2, -1, 0, 0], 'aplist': [-1, 2, 0, -1, 0, -2, -2, 0, 6, -10, 8, 4, -2, 8, 6, -12, 4, 2, -2, -8, 6, 8, -16, -6, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 21175, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '21175.m', 'trace_hash': 574199057551989372}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.0046906313983089647713062679897', 'prec': 110}, 'conductor': 21175, 'gens': [[279610, 54356917, 11]], 'heights': [{'__RealLiteral__': 0, 'data': '9.5352892346627978809462495994', 'prec': 100}], 'lmfdb_label': '21175.m1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.11054178451471391731360294168', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.2161915514542655635309346564033211966', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-3485, 3481, 2]], 'xcoord_integral_points': []}
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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': [3, 0], '29': [1, 0], '31': [3, 0], '37': [3, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21175.m1'}
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ec_torsion_growth • Show schema
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id: 1078128
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '21175.m1', 'torsion': [2, 2]}
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id: 1078129
{'degree': 4, 'field': [20, 0, 5, 0, 1], 'lmfdb_label': '21175.m1', 'torsion': [4]}
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id: 1078132
{'degree': 8, 'field': [-3849, 1155, 3413, -2640, 729, -55, -3, 0, 1], 'lmfdb_label': '21175.m1', 'torsion': [6]}
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id: 1078130
{'degree': 8, 'field': [625, 0, -375, 0, 120, 0, -15, 0, 1], 'lmfdb_label': '21175.m1', 'torsion': [2, 4]}
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id: 1078131
{'degree': 8, 'field': [336611, 26862, -48495, -4548, 3114, 188, -95, -2, 1], 'lmfdb_label': '21175.m1', 'torsion': [2, 4]}
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id: 1078133
{'degree': 16, 'field': [9834496, 0, -9132032, 0, 2873360, 0, -357952, 0, 68149, 0, 3992, 0, 710, 0, -8, 0, 1], 'lmfdb_label': '21175.m1', 'torsion': [8]}
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id: 1078134
{'degree': 16, 'field': [65593801, 0, -102582235, 0, -2103857, 0, 259130, 0, 28249, 0, 155, 0, 487, 0, -10, 0, 1], 'lmfdb_label': '21175.m1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 481954
{'conductor': 21175, 'conductor_valuation': 2, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -3, 'lmfdb_label': '21175.m1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 481955
{'conductor': 21175, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21175.m1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 481956
{'conductor': 21175, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '21175.m1', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1805653
{'adelic_gens': [[57, 166, 164, 55], [1, 2, 2, 5], [217, 4, 216, 5], [3, 4, 8, 11], [101, 4, 202, 9], [1, 4, 0, 1], [48, 1, 43, 0], [1, 0, 4, 1]], 'adelic_image': '220.12.0.?', 'conductor': 21175, 'lmfdb_label': '21175.m1', 'prime': 0}
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id: 98228
{'conductor': 21175, 'elladic_image': '2.3.0.1', 'lmfdb_label': '21175.m1', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 992450
{'lmfdb_iso': '21175.m', 'p': 13, 'prec': 20, 'unit': 495769323701809349032, 'val': 1}
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id: 992452
{'lmfdb_iso': '21175.m', 'p': 17, 'prec': 20, 'unit': 158610713560930863856320, 'val': 1}
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id: 992457
{'lmfdb_iso': '21175.m', 'p': 23, 'prec': 20, 'unit': 392445690970775741585439, 'val': 2}
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id: 992449
{'lmfdb_iso': '21175.m', 'p': 29, 'prec': 20, 'unit': 726780577649604684380165685, 'val': 1}
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id: 992461
{'lmfdb_iso': '21175.m', 'p': 31, 'prec': 20, 'unit': 648832145443703609279680928, 'val': 2}
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id: 992445
{'lmfdb_iso': '21175.m', 'p': 37, 'prec': 20, 'unit': 15058498678943088544907999600, 'val': 2}
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id: 992447
{'lmfdb_iso': '21175.m', 'p': 41, 'prec': 20, 'unit': 2631203668622962946184470585785, 'val': 1}
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id: 992448
{'lmfdb_iso': '21175.m', 'p': 43, 'prec': 20, 'unit': 2217476229921145227334310167372, 'val': 1}
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id: 992459
{'lmfdb_iso': '21175.m', 'p': 47, 'prec': 20, 'unit': 35926997910503796659218676363600, 'val': 1}
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id: 992454
{'lmfdb_iso': '21175.m', 'p': 53, 'prec': 20, 'unit': 159729973121407775098037187878033, 'val': 1}
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id: 992455
{'lmfdb_iso': '21175.m', 'p': 59, 'prec': 20, 'unit': 4265937546393839636500732143763386, 'val': 1}
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id: 992460
{'lmfdb_iso': '21175.m', 'p': 61, 'prec': 20, 'unit': 7271866003606436251824772753587694, 'val': 1}
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id: 992444
{'lmfdb_iso': '21175.m', 'p': 67, 'prec': 20, 'unit': 33153042802655051127485546469299322, 'val': 1}
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id: 992446
{'lmfdb_iso': '21175.m', 'p': 71, 'prec': 20, 'unit': 68417972882806200371776879180848733, 'val': 1}
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id: 992456
{'lmfdb_iso': '21175.m', 'p': 73, 'prec': 20, 'unit': 223157666784223729450967026540724939, 'val': 1}
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id: 992451
{'lmfdb_iso': '21175.m', 'p': 79, 'prec': 20, 'unit': 1004288042419418774700321919609327880, 'val': 1}
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id: 992453
{'lmfdb_iso': '21175.m', 'p': 83, 'prec': 20, 'unit': 1153499006221140463490404350983179562, 'val': 1}
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id: 992458
{'lmfdb_iso': '21175.m', 'p': 89, 'prec': 20, 'unit': 2368069819711701801243818398176496278, 'val': 1}
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id: 992443
{'lmfdb_iso': '21175.m', 'p': 97, 'prec': 20, 'unit': 50402105972221890277650276269179268454, 'val': 1}