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ec_curvedata • Show schema
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{'Ciso': '215985bm', 'Clabel': '215985bm2', 'Cnumber': 2, 'abc_quality': 0.9453840558266575, 'absD': 62231626218155625, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 31416, 'ainvs': [1, 0, 1, -473113, -124717969], 'analytic_rank': 0, 'bad_primes': [3, 5, 7, 11, 17], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 215985, 'degree': 2621440, 'elladic_images': ['8.24.0.10'], 'faltings_height': {'__RealLiteral__': 0, 'data': '2.0670090832133275686536511775', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 50, 'isogeny_degrees': [1, 2, 4], 'jinv': [6610905152742241, 35128130625], 'lmfdb_iso': '215985.by', 'lmfdb_label': '215985.by3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -3910, 93347], 'min_quad_twist_disc': -11, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.24.0.e.2', '44.24.0-4.b.1.3', '68.24.0.c.1', '88.48.0.?', '136.48.0.?', '168.48.0.?', '748.48.0.?', '1496.96.0.?', '1848.96.0.?', '2856.96.1.?', '31416.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.86806144681414229662267938852', 'prec': 103}, 'szpiro_ratio': 4.1370199913443955, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 1, -1, 1, 1, -1, -3, 1, 1, 0, -1, 2, -1, 1, -1, -1, 1, 4, -1], 'aplist': [1, 1, 1, -1, 0, 2, -1, 4, -8, -6, 0, -10, 6, 4, 0, 6, -4, -6, 4, 8, -2, 16, 12, -6, 10], 'class_deg': 8, 'class_size': 6, 'conductor': 215985, 'isogeny_matrix': [[1, 2, 4, 8, 8, 4], [2, 1, 2, 4, 4, 2], [4, 2, 1, 2, 2, 4], [8, 4, 2, 1, 4, 8], [8, 4, 2, 4, 1, 8], [4, 2, 4, 8, 8, 1]], 'lmfdb_iso': '215985.by', 'trace_hash': 18480487072940706}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.016018384799493568183554289039', 'prec': 107}, 'conductor': 215985, 'gens': [], 'heights': [], 'lmfdb_label': '215985.by3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.18209472873186142636035733678', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9135156597097828217657173884752353645', 'prec': 130}, 'tamagawa_product': 256, 'torsion_generators': [[-419, 209, 1], [-375, 187, 1]], 'xcoord_integral_points': [-419, -375]}
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lmfdb_label 215985.by3 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9417888
{'degree': 2, 'field': [3, -1, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 4]}
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id: 9417889
{'degree': 4, 'field': [38, 30, -29, -2, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 4]}
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id: 9417890
{'degree': 4, 'field': [49, 0, 3, 0, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 4]}
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id: 9417891
{'degree': 4, 'field': [64, 0, -5, 0, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 8]}
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id: 9417892
{'degree': 8, 'field': [53, -262, 492, -490, 321, -94, 36, -4, 1], 'lmfdb_label': '215985.by3', 'torsion': [4, 4]}
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id: 9417893
{'degree': 8, 'field': [2388, -2052, 2602, -1150, 701, -154, 56, -4, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 8]}
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id: 9417894
{'degree': 8, 'field': [2923259, -1606462, 215984, -588, 1659, -279, -17, -2, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 6]}
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id: 9417896
{'degree': 16, 'field': [561001, 0, -4876036, 0, 19052878, 0, 480936, 0, -44877, 0, -7848, 0, 502, 0, -28, 0, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 8]}
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id: 9417899
{'degree': 16, 'field': [1531575, -379350, 450180, -292026, 559119, -600556, 377222, -157168, 47900, -8782, 5162, -2336, 814, -224, 52, -8, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 12]}
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id: 9417897
{'degree': 16, 'field': [5702544, 0, -8216448, 0, 5398780, 0, -1960944, 0, 416985, 0, -50800, 0, 3306, 0, -96, 0, 1], 'lmfdb_label': '215985.by3', 'torsion': [4, 8]}
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id: 9417898
{'degree': 16, 'field': [71836395, -196604760, 215742699, -44456706, 38136073, -20356694, 8872598, -1737678, 369457, 44324, -9032, -1006, 1108, -462, 86, -8, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 16]}
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id: 9417895
{'degree': 16, 'field': [34267192996, 0, -4230122248, 0, -519458080, 0, 77109492, 0, 744989, 0, -336432, 0, 10670, 0, -172, 0, 1], 'lmfdb_label': '215985.by3', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 5353308
{'conductor': 215985, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '215985.by3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 5353309
{'conductor': 215985, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '215985.by3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 4}
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id: 5353310
{'conductor': 215985, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '215985.by3', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 5353311
{'conductor': 215985, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '215985.by3', 'prime': 11, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 5353312
{'conductor': 215985, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '215985.by3', 'prime': 17, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 3044152
{'adelic_gens': [[5, 4, 31412, 31413], [20945, 2860, 0, 1], [27391, 17138, 28710, 11419], [18569, 12144, 3564, 9989], [1, 0, 8, 1], [2861, 27852, 28534, 683], [8977, 2860, 0, 1], [8567, 0, 0, 31415], [31409, 8, 31408, 9], [1, 8, 0, 1]], 'adelic_image': '31416.192.1.?', 'conductor': 215985, 'lmfdb_label': '215985.by3', 'prime': 0}
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id: 794302
{'conductor': 215985, 'elladic_image': '8.24.0.10', 'lmfdb_label': '215985.by3', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 215985.by does not appear in ec_padic