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ec_curvedata • Show schema
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{'Ciso': '12480t', 'Clabel': '12480t2', 'Cnumber': 2, 'abc_quality': 1.0142518435034014, 'absD': 213206722560000, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 312, 'ainvs': [0, 1, 0, -608401, 182451599], 'analytic_rank': 0, 'bad_primes': [2, 3, 5, 13], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 12480, 'degree': 122880, 'elladic_images': ['8.48.0.135'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9175712558485720435953988666', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'intrinsic_torsion': 1, 'iso_nlabel': 53, 'isogeny_degrees': [1, 2, 4], 'jinv': [1520107298839022416, 13013105625], 'lmfdb_iso': '12480.cb', 'lmfdb_label': '12480.cb4', 'lmfdb_number': 4, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -152100, 22882500], 'min_quad_twist_disc': 8, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.d.1.1', '12.24.0.c.1', '24.96.0-24.g.2.5', '104.96.0.?', '312.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 4, 'num_int_pts': 3, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'serre_invariants': [[2, 2, 1], [3, 4, 4160], [5, 6, 2496], [13, 14, 960]], 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '1.1088995451953025159419613916', 'prec': 100}, 'szpiro_ratio': 5.467558819722957, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 4, 0, -1, 0, -1, 0, 2, 0, 4, 0], 'aplist': [0, 1, -1, 0, 4, -1, 2, 4, 8, -6, 8, -6, 2, 12, -8, 2, -12, 2, -12, 16, 10, 8, 12, 18, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 12480, 'isogeny_matrix': [[1, 8, 4, 2, 4, 8], [8, 1, 2, 4, 8, 4], [4, 2, 1, 2, 4, 2], [2, 4, 2, 1, 2, 4], [4, 8, 4, 2, 1, 8], [8, 4, 2, 4, 8, 1]], 'lmfdb_iso': '12480.cb', 'trace_hash': 2255529763374304303}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.021598260246116541808895385505', 'prec': 107}, 'conductor': 12480, 'gens': [], 'heights': [], 'lmfdb_label': '12480.cb4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.50538985838809066387518692499', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '3.0323391503285439832511215499207049607', 'prec': 130}, 'tamagawa_product': 96, 'torsion_generators': [[449, 0, 1], [451, 0, 1]], 'xcoord_integral_points': [-901, 449, 451]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': [0, 0], '13': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '12480.cb4'}
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ec_torsion_growth • Show schema
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id: 643191
{'degree': 2, 'field': [-2, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 4]}
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id: 643192
{'degree': 4, 'field': [1, 0, 4, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 4]}
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id: 643193
{'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 4]}
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id: 643195
{'degree': 8, 'field': [-23, 76, 16, -164, 33, 56, -14, -4, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 8]}
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id: 643198
{'degree': 8, 'field': [-3, 0, 14, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 6]}
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id: 643194
{'degree': 8, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [4, 4]}
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id: 643196
{'degree': 8, 'field': [81, 0, 0, 0, 31, 0, 0, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 8]}
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id: 643197
{'degree': 8, 'field': [361, 0, 326, 0, 102, 0, 14, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 8]}
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id: 643200
{'degree': 16, 'field': [961, 8184, 24344, 19640, -26272, -18744, 39830, -26508, 7747, 24, -770, -32, 258, -140, 46, -8, 1], 'lmfdb_label': '12480.cb4', 'torsion': [4, 8]}
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id: 643202
{'degree': 16, 'field': [4225, 0, 1100, 0, -5600, 0, -1128, 0, 1062, 0, -372, 0, 124, 0, -16, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 12]}
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id: 643201
{'degree': 16, 'field': [6561, 0, 0, 0, -2511, 0, 0, 0, 880, 0, 0, 0, -31, 0, 0, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [4, 8]}
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id: 643199
{'degree': 16, 'field': [407241, -1774980, 2771946, -441360, 748878, -103740, 155334, 103020, 24763, -120, -10102, -180, 1152, 0, -52, 0, 1], 'lmfdb_label': '12480.cb4', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 269891
{'conductor': 12480, 'conductor_valuation': 6, 'discriminant_valuation': 14, 'j_denominator_valuation': 0, 'kodaira_symbol': -8, 'lmfdb_label': '12480.cb4', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 269892
{'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '12480.cb4', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 269893
{'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12480.cb4', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 269894
{'conductor': 12480, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '12480.cb4', 'prime': 13, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1746776
{'adelic_gens': [[1, 0, 8, 1], [5, 4, 308, 309], [1, 8, 0, 1], [151, 72, 104, 187], [215, 6, 306, 307], [145, 8, 268, 33], [5, 80, 2, 235], [305, 8, 304, 9]], 'adelic_image': '312.192.1.?', 'conductor': 12480, 'lmfdb_label': '12480.cb4', 'prime': 0}
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id: 59412
{'conductor': 12480, 'elladic_image': '8.48.0.135', 'lmfdb_label': '12480.cb4', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 12480.cb does not appear in ec_padic
