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ec_curvedata • Show schema
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{'Ciso': '90b', 'Clabel': '90b1', 'Cnumber': 1, 'abc_quality': 0.9730541653249261, 'absD': 8640, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 120, 'ainvs': [1, -1, 1, -8, 11], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 90, 'degree': 8, 'elladic_images': ['2.3.0.1', '3.8.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.51836172070932770628692715580', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-1860867, 320], 'lmfdb_iso': '90.b', 'lmfdb_label': '90.b3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 0, -69, -235], 'min_quad_twist_disc': -3, 'modell_images': ['2B', '3B.1.1'], 'modm_images': ['2.3.0.a.1', '3.8.0-3.a.1.2', '6.24.0-6.a.1.4', '24.48.0-24.cd.1.15', '30.48.0-30.b.1.4', '40.6.0.e.1', '120.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.79301479287635512913573846503', 'prec': 107}, 'szpiro_ratio': 3.998515981114699, 'torsion': 6, 'torsion_primes': [2, 3], 'torsion_structure': [6]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, 1, -1, 0, 2, 1, 0, -1, -6, 0, -4, 2, 0, 1, 6, 0, -4, -1], 'aplist': [1, 0, -1, 2, -6, -4, 6, -4, 0, 6, -4, 8, 0, 8, 0, 6, -6, 2, -4, 12, -10, -4, -12, -12, 2], 'class_deg': 6, 'class_size': 4, 'conductor': 90, 'isogeny_matrix': [[1, 3, 6, 2], [3, 1, 2, 6], [6, 2, 1, 3], [2, 6, 3, 1]], 'lmfdb_iso': '90.b', 'trace_hash': 2284528933461194068}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '2.8199620894963716974818925273', 'prec': 100}, 'conductor': 90, 'gens': [], 'heights': [], 'lmfdb_label': '90.b3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '3.9710942585413486372981289183', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.3236980861804495457660429727621209354', 'prec': 130}, 'tamagawa_product': 12, 'torsion_generators': [[3, 1, 1]], 'xcoord_integral_points': [-3, 1, 3]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 0], '3': 'a', '5': [0, 0]}, 'iwp0': 5, 'lmfdb_label': '90.b3'}
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ec_torsion_growth • Show schema
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id: 3127
{'degree': 2, 'field': [4, -1, 1], 'lmfdb_label': '90.b3', 'torsion': [2, 6]}
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id: 3128
{'degree': 4, 'field': [-2, 4, -3, -2, 1], 'lmfdb_label': '90.b3', 'torsion': [12]}
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id: 3129
{'degree': 6, 'field': [36, -18, -9, 3, 6, -3, 1], 'lmfdb_label': '90.b3', 'torsion': [3, 6]}
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id: 3130
{'degree': 8, 'field': [16, 0, -14, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '90.b3', 'torsion': [2, 12]}
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id: 3131
{'degree': 8, 'field': [16, 32, 20, -28, 4, -2, 5, -2, 1], 'lmfdb_label': '90.b3', 'torsion': [2, 12]}
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id: 3132
{'degree': 9, 'field': [144, -216, 108, -90, 18, 0, -15, 9, -3, 1], 'lmfdb_label': '90.b3', 'torsion': [18]}
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id: 3133
{'degree': 12, 'field': [4, -42, 177, -400, 585, -642, 551, -366, 195, -80, 27, -6, 1], 'lmfdb_label': '90.b3', 'torsion': [6, 6]}
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id: 3134
{'degree': 16, 'field': [-32, 128, -32, -608, 1124, -1408, 2048, -2192, 844, 472, -556, 200, -61, 28, -2, -4, 1], 'lmfdb_label': '90.b3', 'torsion': [24]}
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id: 3135
{'degree': 18, 'field': [64, -96, 240, -552, 936, -1392, 1986, -2586, 2862, -2909, 2715, -2112, 1554, -954, 474, -174, 48, -9, 1], 'lmfdb_label': '90.b3', 'torsion': [2, 18]}
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ec_localdata • Show schema
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id: 515
{'conductor': 90, 'conductor_valuation': 1, 'discriminant_valuation': 6, 'j_denominator_valuation': 6, 'kodaira_symbol': 10, 'lmfdb_label': '90.b3', 'prime': 2, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 6}
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id: 516
{'conductor': 90, 'conductor_valuation': 2, 'discriminant_valuation': 3, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '90.b3', 'prime': 3, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 517
{'conductor': 90, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '90.b3', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1666126
{'adelic_gens': [[1, 12, 0, 1], [32, 11, 45, 88], [61, 12, 6, 73], [109, 12, 108, 13], [11, 2, 70, 111], [1, 6, 6, 37], [10, 3, 21, 112], [1, 0, 12, 1], [39, 58, 86, 101]], 'adelic_image': '120.96.1.?', 'conductor': 90, 'lmfdb_label': '90.b3', 'prime': 0}
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id: 292
{'conductor': 90, 'elladic_image': '2.3.0.1', 'lmfdb_label': '90.b3', 'modell_image': '2B', 'prime': 2}
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id: 293
{'conductor': 90, 'elladic_image': '3.8.0.1', 'lmfdb_label': '90.b3', 'modell_image': '3B.1.1', 'prime': 3}
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lmfdb_iso 90.b does not appear in ec_padic