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ec_curvedata • Show schema
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{'Ciso': '27a', 'Clabel': '27a3', 'Cnumber': 3, 'absD': 27, 'ainvs': [0, 0, 1, 0, 0], 'analytic_rank': 0, 'bad_primes': [3], 'class_deg': 27, 'class_size': 4, 'cm': -3, 'conductor': 27, 'degree': 3, 'elladic_images': ['27.1944.55.31'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-1.0464643562610104921410578866', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 0, 'isogeny_degrees': [1, 3, 9], 'jinv': [0, 1], 'lmfdb_iso': '27.a', 'lmfdb_label': '27.a4', 'lmfdb_number': 4, 'manin_constant': 3, 'min_quad_twist_ainvs': [0, 0, 1, 0, 0], 'min_quad_twist_disc': 1, 'modell_images': ['3Cs.1.1'], 'nonmax_primes': [3], 'nonmax_rad': 3, 'num_bad_primes': 1, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': True, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.3211174284280379149898691958', 'prec': 103}, 'szpiro_ratio': 3.261859507142915, 'torsion': 3, 'torsion_primes': [3], 'torsion_structure': [3]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 0, -2, 0, 0, -1, 0, 0, 0, 0, 0, 5, 0, 0, 4, 0, 0, -7, 0], 'aplist': [0, 0, 0, -1, 0, 5, 0, -7, 0, 0, -4, 11, 0, 8, 0, 0, 0, -1, 5, 0, -7, 17, 0, 0, -19], 'class_deg': 27, 'class_size': 4, 'conductor': 27, 'isogeny_matrix': [[1, 27, 3, 9], [27, 1, 9, 3], [3, 9, 1, 3], [9, 3, 3, 1]], 'lmfdb_iso': '27.a', 'trace_hash': 903291523394155081}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '8.1086282640626946408463030204', 'prec': 100}, 'conductor': 27, 'gens': [], 'heights': [], 'lmfdb_label': '27.a4', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.2999162508563498719410684990', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.58887958342848331910456316654932546833', 'prec': 133}, 'tamagawa_product': 1, 'torsion_generators': [[0, 0, 1]], 'xcoord_integral_points': [0]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 5, 0], '3': 'a'}, 'iwp0': 5, 'lmfdb_label': '27.a4'}
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ec_torsion_growth • Show schema
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id: 655
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '27.a4', 'torsion': [3, 3]}
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id: 656
{'degree': 3, 'field': [-2, 0, 0, 1], 'lmfdb_label': '27.a4', 'torsion': [6]}
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id: 657
{'degree': 3, 'field': [-1, -3, 0, 1], 'lmfdb_label': '27.a4', 'torsion': [9]}
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id: 658
{'degree': 6, 'field': [1, -3, 0, 5, 0, -3, 1], 'lmfdb_label': '27.a4', 'torsion': [6, 6]}
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id: 659
{'degree': 6, 'field': [1, 0, 0, -1, 0, 0, 1], 'lmfdb_label': '27.a4', 'torsion': [3, 9]}
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id: 660
{'degree': 9, 'field': [1, -6, 15, -15, -3, 12, -6, 3, -3, 1], 'lmfdb_label': '27.a4', 'torsion': [18]}
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id: 661
{'degree': 12, 'field': [-2, 0, 12, 4, -18, -12, 0, 12, 12, -2, -6, 0, 1], 'lmfdb_label': '27.a4', 'torsion': [12]}
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id: 662
{'degree': 12, 'field': [1, -6, 21, -44, 66, -81, 84, -72, 54, -35, 18, -6, 1], 'lmfdb_label': '27.a4', 'torsion': [3, 21]}
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id: 663
{'degree': 18, 'field': [1, 0, 0, 6, 0, 0, 33, 0, 0, 20, 0, 0, 15, 0, 0, -3, 0, 0, 1], 'lmfdb_label': '27.a4', 'torsion': [9, 9]}
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id: 664
{'degree': 18, 'field': [3, 0, -9, 0, 18, -9, -6, 0, 0, 27, -63, 72, -21, -63, 105, -81, 36, -9, 1], 'lmfdb_label': '27.a4', 'torsion': [6, 18]}
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ec_localdata • Show schema
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{'conductor': 27, 'conductor_valuation': 3, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '27.a4', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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{'conductor': 27, 'elladic_image': '27.1944.55.31', 'lmfdb_label': '27.a4', 'modell_image': '3Cs.1.1', 'prime': 3}
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lmfdb_iso 27.a does not appear in ec_padic