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ec_curvedata • Show schema
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{'Ciso': '30a', 'Clabel': '30a6', 'Cnumber': 6, 'abc_quality': 1.0522127879225598, 'absD': 9000000, 'adelic_genus': 5, 'adelic_index': 384, 'adelic_level': 120, 'ainvs': [1, 0, 1, -334, -2368], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 12, 'class_size': 8, 'cm': 0, 'conductor': 30, 'degree': 12, 'elladic_images': ['8.12.0.1', '3.8.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626083', 'prec': 103}, 'faltings_index': 5, 'faltings_ratio': 6, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [4102915888729, 9000000], 'lmfdb_iso': '30.a', 'lmfdb_label': '30.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 1, -334, -2368], 'min_quad_twist_disc': 1, 'modell_images': ['2Cs', '3B.1.2'], 'modm_images': ['2.6.0.a.1', '3.8.0-3.a.1.1', '6.48.0-6.a.1.2', '8.12.0-2.a.1.1', '12.96.0-12.a.1.15', '20.12.0-2.a.1.1', '24.192.1-24.cp.2.4', '40.24.0-40.a.1.3', '60.192.1-60.h.3.4', '120.384.5.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.21759239493637902558062626083', 'prec': 103}, 'szpiro_ratio': 8.538969007156295, '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, -4, -1, 1, 1, 0, 1, 2, 4, -1, 1, 6, -1, -4, -1], 'aplist': [-1, 1, -1, -4, 0, 2, 6, -4, 0, -6, 8, 2, -6, -4, 0, -6, 0, -10, -4, 0, 2, 8, 12, 18, 2], 'class_deg': 12, 'class_size': 8, 'conductor': 30, 'isogeny_matrix': [[1, 4, 2, 12, 3, 6, 4, 12], [4, 1, 2, 3, 12, 6, 4, 12], [2, 2, 1, 6, 6, 3, 2, 6], [12, 3, 6, 1, 4, 2, 12, 4], [3, 12, 6, 4, 1, 2, 12, 4], [6, 6, 3, 2, 2, 1, 6, 2], [4, 4, 2, 12, 12, 6, 1, 3], [12, 12, 6, 4, 4, 2, 3, 1]], 'lmfdb_iso': '30.a', 'trace_hash': 148452494971348580}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.64714507017305323183191669441', 'prec': 103}, 'conductor': 30, 'gens': [], 'heights': [], 'lmfdb_label': '30.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.1173160864138321498160760446', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.55865804320691607490803802232401598477', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-11, 5, 1], [21, -11, 1]], 'xcoord_integral_points': [-11, 21]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 0], '3': [1, 1], '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '30.a3'}
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ec_torsion_growth • Show schema
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id: 757
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 6]}
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id: 758
{'degree': 3, 'field': [-3, 0, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 6]}
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id: 760
{'degree': 4, 'field': [4, 0, -6, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 4]}
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id: 761
{'degree': 4, 'field': [4, 0, -2, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 12]}
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id: 759
{'degree': 4, 'field': [4, 0, 1, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 4]}
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id: 762
{'degree': 6, 'field': [3, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [6, 6]}
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id: 764
{'degree': 8, 'field': [1, 0, -3, 0, 8, 0, -3, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 12]}
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id: 763
{'degree': 8, 'field': [16, 0, 24, 0, 32, 0, 6, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 12]}
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id: 766
{'degree': 12, 'field': [-1151, 1044, 1764, -540, 966, -72, -306, 0, 120, -12, -18, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 12]}
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id: 765
{'degree': 12, 'field': [4, 0, -87, 0, 663, 0, 145, 0, -3, 0, 3, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 12]}
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id: 767
{'degree': 12, 'field': [25, -180, 372, 432, 186, 72, -50, -72, 24, 0, -6, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [6, 12]}
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id: 768
{'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [4, 12]}
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id: 769
{'degree': 16, 'field': [6, 36, 84, 36, 49, 4, 53, -42, 31, -40, -2, 8, -11, 0, 5, -2, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 8]}
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id: 770
{'degree': 16, 'field': [16, 0, -256, 0, 1240, 0, -1824, 0, 384, 0, -144, 0, 70, 0, -16, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 8]}
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id: 771
{'degree': 16, 'field': [16, 0, -128, 0, 904, 0, -896, 0, 640, 0, -176, 0, 34, 0, -8, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 24]}
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id: 772
{'degree': 18, 'field': [27, 0, 0, -90, 0, 0, 147, 0, 0, -120, 0, 0, 49, 0, 0, -10, 0, 0, 1], 'lmfdb_label': '30.a3', 'torsion': [2, 18]}
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ec_localdata • Show schema
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id: 99
{'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '30.a3', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 100
{'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '30.a3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 101
{'conductor': 30, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '30.a3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1665935
{'adelic_gens': [[1, 12, 0, 1], [47, 6, 94, 115], [97, 12, 114, 7], [61, 12, 6, 73], [109, 12, 108, 13], [9, 4, 104, 113], [1, 0, 12, 1], [97, 6, 0, 1]], 'adelic_image': '120.384.5.?', 'conductor': 30, 'lmfdb_label': '30.a3', 'prime': 0}
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id: 59
{'conductor': 30, 'elladic_image': '8.12.0.1', 'lmfdb_label': '30.a3', 'modell_image': '2Cs', 'prime': 2}
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id: 60
{'conductor': 30, 'elladic_image': '3.8.0.2', 'lmfdb_label': '30.a3', 'modell_image': '3B.1.2', 'prime': 3}
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lmfdb_iso 30.a does not appear in ec_padic