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ec_curvedata • Show schema
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{'Ciso': '21879i', 'Clabel': '21879i2', 'Cnumber': 2, 'abc_quality': 0.8608596561528015, 'absD': 40099546773, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 884, 'ainvs': [1, -1, 1, 238, 9470], 'analytic_rank': 1, 'bad_primes': [3, 11, 13, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 21879, 'degree': 21504, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.71467353553569420947689330620', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2], 'jinv': [2053225511, 55006237], 'lmfdb_iso': '21879.a', 'lmfdb_label': '21879.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, 26, -351], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '52.6.0.a.1', '68.6.0.c.1', '884.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.2274740253234367923781052867', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 117], [3, 2, 2431], [11, 12, 1989], [13, 14, 1683], [17, 18, 1287]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.16536739120163936377927068774', 'prec': 103}, 'szpiro_ratio': 3.1868920522200406, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, 0, -1, -4, 0, 0, 3, 0, 4, -1, 0, 1, 0, 0, -1, -1, 0, 4, 4], 'aplist': [-1, 0, -4, 0, -1, 1, -1, 4, 6, 2, -4, 8, 0, -8, -8, -10, -4, 10, -4, -16, 0, -6, 4, 18, 8], 'class_deg': 2, 'class_size': 2, 'conductor': 21879, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '21879.a', 'trace_hash': 1822342059199939554}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.23946522498369973643774125556', 'prec': 103}, 'conductor': 21879, 'gens': [[13, 114, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.2274740253234367923781052867', 'prec': 100}], 'lmfdb_label': '21879.a2', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.86278337855433511158817069414', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.1180883733124885781934294544077594080', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[-69, 65, 2]], 'xcoord_integral_points': [13, 21]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 1], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '21879.a2'}
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ec_torsion_growth • Show schema
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id: 1112404
{'degree': 2, 'field': [13, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 2]}
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id: 1112405
{'degree': 4, 'field': [-104, -44, -1, -1, 1], 'lmfdb_label': '21879.a2', 'torsion': [4]}
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id: 1112408
{'degree': 8, 'field': [-243, 0, -73, 0, -54, 0, 0, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [6]}
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id: 1112407
{'degree': 8, 'field': [3636, 6084, 1662, -1638, 217, -78, 8, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 4]}
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id: 1112406
{'degree': 8, 'field': [52009, -2828, 12872, 2764, -518, 68, 8, -4, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 4]}
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id: 1112409
{'degree': 16, 'field': [116985856, 0, -180488365824, 0, -34193218384, 0, -2451051616, 0, -84277128, 0, -1294696, 0, -2037, 0, 152, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [8]}
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id: 1112410
{'degree': 16, 'field': [405659881, 0, 580295834, 0, 180439489, 0, 28117992, 0, 2336658, 0, 125694, 0, 4624, 0, 104, 0, 1], 'lmfdb_label': '21879.a2', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 499233
{'conductor': 21879, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '21879.a2', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 499234
{'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '21879.a2', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 499235
{'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '21879.a2', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 499236
{'conductor': 21879, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '21879.a2', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1810368
{'adelic_gens': [[1, 0, 4, 1], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [664, 225, 221, 664], [881, 4, 880, 5], [105, 4, 210, 9], [342, 1, 271, 0]], 'adelic_image': '884.12.0.?', 'conductor': 21879, 'lmfdb_label': '21879.a2', 'prime': 0}
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id: 101261
{'conductor': 21879, 'elladic_image': '2.3.0.1', 'lmfdb_label': '21879.a2', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 1028926
{'lmfdb_iso': '21879.a', 'p': 5, 'prec': 20, 'unit': 88630814835457, 'val': -1}
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id: 1028910
{'lmfdb_iso': '21879.a', 'p': 19, 'prec': 20, 'unit': 1161357730587923302365918, 'val': 1}
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id: 1028922
{'lmfdb_iso': '21879.a', 'p': 23, 'prec': 20, 'unit': 5691625365905554721342380, 'val': 1}
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id: 1028917
{'lmfdb_iso': '21879.a', 'p': 29, 'prec': 20, 'unit': 6014864411543843273618791948, 'val': 1}
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id: 1028915
{'lmfdb_iso': '21879.a', 'p': 31, 'prec': 20, 'unit': 12429900352485779307515703778, 'val': 1}
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id: 1028913
{'lmfdb_iso': '21879.a', 'p': 37, 'prec': 20, 'unit': 517083515053539846888598838871, 'val': 1}
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id: 1028916
{'lmfdb_iso': '21879.a', 'p': 43, 'prec': 20, 'unit': 6629303841109330068883673233930, 'val': 1}
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id: 1028924
{'lmfdb_iso': '21879.a', 'p': 47, 'prec': 20, 'unit': 23134975839118315163966190291810, 'val': 1}
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id: 1028921
{'lmfdb_iso': '21879.a', 'p': 53, 'prec': 20, 'unit': 448237395078664131077290461837861, 'val': 1}
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id: 1028919
{'lmfdb_iso': '21879.a', 'p': 59, 'prec': 20, 'unit': 694703306860245605651977030349127, 'val': 1}
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id: 1028925
{'lmfdb_iso': '21879.a', 'p': 61, 'prec': 20, 'unit': 5646291236587564310783784935292218, 'val': 1}
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id: 1028912
{'lmfdb_iso': '21879.a', 'p': 67, 'prec': 20, 'unit': 25022266175143124230604257243859895, 'val': 1}
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id: 1028914
{'lmfdb_iso': '21879.a', 'p': 71, 'prec': 20, 'unit': 85145545242892668933731675951883485, 'val': 1}
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id: 1028918
{'lmfdb_iso': '21879.a', 'p': 79, 'prec': 20, 'unit': 844775412877483342575112443593790074, 'val': 1}
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id: 1028920
{'lmfdb_iso': '21879.a', 'p': 83, 'prec': 20, 'unit': 84750936757969634375812278286275670, 'val': 1}
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id: 1028923
{'lmfdb_iso': '21879.a', 'p': 89, 'prec': 20, 'unit': 1882516932711931207706316904346152054, 'val': 1}
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id: 1028911
{'lmfdb_iso': '21879.a', 'p': 97, 'prec': 20, 'unit': 22161846157811881962524003777282814648, 'val': 1}