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ec_curvedata • Show schema
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{'Ciso': '219912bj', 'Clabel': '219912bj2', 'Cnumber': 2, 'abc_quality': 0.8841428566887771, 'absD': 361310025517056, 'adelic_genus': 0, 'adelic_index': 12, 'adelic_level': 4488, 'ainvs': [0, 1, 0, -40392, 2974320], 'analytic_rank': 0, 'bad_primes': [2, 3, 7, 11, 17], 'class_deg': 2, 'class_size': 2, 'cm': 0, 'conductor': 219912, 'degree': 829440, 'elladic_images': ['2.3.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.5524393094303764136820341202', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 44, 'isogeny_degrees': [1, 2], 'jinv': [30248395634, 1499553], 'lmfdb_iso': '219912.bs', 'lmfdb_label': '219912.bs1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -824, -8436], 'min_quad_twist_disc': -7, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '132.6.0.?', '136.6.0.?', '4488.12.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 5, 'num_int_pts': 1, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 4, 833], [3, 4, 73304], [7, 26, 4488], [11, 12, 19992], [17, 18, 12936]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055900680610563439169771696193', 'prec': 110}, 'szpiro_ratio': 3.5308389388777863, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, 2, 0, 1, 0, -2, 0], 'aplist': [0, 1, 2, 0, -1, 0, 1, -2, 2, 10, -8, -6, -2, 2, 0, -12, -10, -10, -4, 6, 0, -10, 4, 10, 14], 'class_deg': 2, 'class_size': 2, 'conductor': 219912, 'isogeny_matrix': [[1, 2], [2, 1]], 'lmfdb_iso': '219912.bs', 'trace_hash': 2242371204190673163}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.044829959740617515636648592433', 'prec': 107}, 'conductor': 219912, 'gens': [], 'heights': [], 'lmfdb_label': '219912.bs1', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.53084674378764867998262416839', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.1850804627258920798957450103664161501', 'prec': 130}, 'tamagawa_product': 24, 'torsion_generators': [[135, 0, 1]], 'xcoord_integral_points': [135]}
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lmfdb_label 219912.bs1 does not appear in ec_iwasawa
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ec_torsion_growth • Show schema
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id: 9575500
{'degree': 2, 'field': [-34, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 2]}
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id: 9575501
{'degree': 4, 'field': [6664, 0, -203, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [4]}
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id: 9575504
{'degree': 8, 'field': [-80514, 18144, 54378, 11190, 5370, 42, 142, -2, 1], 'lmfdb_label': '219912.bs1', 'torsion': [6]}
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id: 9575503
{'degree': 8, 'field': [40857664, 0, -591872, 0, 33320, 0, -272, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 4]}
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id: 9575502
{'degree': 8, 'field': [43848814, -5737636, -3918866, 54544, 76199, 544, -494, -4, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 4]}
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id: 9575505
{'degree': 16, 'field': [251127267876, 0, -112145985288, 0, 18406357980, 0, -1375013448, 0, 49938061, 0, -1180174, 0, 21438, 0, -238, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [8]}
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id: 9575506
{'degree': 16, 'field': [28362995278864, 0, -2011835139296, 0, 34234255648, 0, -55733072, 0, -9199448, 0, 294712, 0, -5780, 0, -68, 0, 1], 'lmfdb_label': '219912.bs1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 5453126
{'conductor': 219912, 'conductor_valuation': 3, 'discriminant_valuation': 11, 'j_denominator_valuation': 0, 'kodaira_symbol': -2, 'lmfdb_label': '219912.bs1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 5453127
{'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '219912.bs1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 5453128
{'conductor': 219912, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '219912.bs1', 'prime': 7, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 5453129
{'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '219912.bs1', 'prime': 11, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 5453130
{'conductor': 219912, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '219912.bs1', 'prime': 17, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 3068618
{'adelic_gens': [[1, 0, 4, 1], [409, 4, 818, 9], [2993, 4, 1498, 9], [3, 4, 8, 11], [1, 2, 2, 5], [1, 4, 0, 1], [2, 1, 2243, 0], [2114, 1, 3431, 0], [3929, 562, 560, 3927], [4485, 4, 4484, 5]], 'adelic_image': '4488.12.0.?', 'conductor': 219912, 'lmfdb_label': '219912.bs1', 'prime': 0}
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id: 807129
{'conductor': 219912, 'elladic_image': '2.3.0.1', 'lmfdb_label': '219912.bs1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 219912.bs does not appear in ec_padic