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ec_curvedata • Show schema
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{'Ciso': '2166b', 'Clabel': '2166b4', 'Cnumber': 4, 'abc_quality': 1.0101536552434738, 'absD': 39839668543190898, 'adelic_genus': 1, 'adelic_index': 96, 'adelic_level': 456, 'ainvs': [1, 1, 0, -150905, 24459183], 'analytic_rank': 0, 'bad_primes': [2, 3, 19], 'class_deg': 6, 'class_size': 4, 'cm': 0, 'conductor': 2166, 'degree': 25920, 'elladic_images': ['8.6.0.5', '3.4.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.9242951258132956358384573460', 'prec': 100}, 'faltings_index': 3, 'faltings_ratio': 6, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 3, 6], 'jinv': [-8078253774625, 846825858], 'lmfdb_iso': '2166.a', 'lmfdb_label': '2166.a2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, -418, -3610], 'min_quad_twist_disc': -19, 'modell_images': ['2B', '3B'], 'modm_images': ['2.3.0.a.1', '3.4.0.a.1', '6.12.0.a.1', '8.6.0.a.1', '12.24.0-6.a.1.11', '24.48.0-24.p.1.12', '57.8.0-3.a.1.2', '114.24.0.?', '228.48.0.?', '456.96.1.?'], 'nonmax_primes': [2, 3], 'nonmax_rad': 6, 'num_bad_primes': 3, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.45207563623007540583394363006', 'prec': 103}, 'szpiro_ratio': 6.191323749077597, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, -1, -1, 1, 0, 1, -4, -1, 1, 0, 0, -1, 4, 4, 0, 1, 6, -1, 0, 0], 'aplist': [-1, -1, 0, -4, 0, 4, 6, 0, -6, -6, -2, 4, -6, -4, 6, -6, 12, 14, -8, 0, 14, 10, -12, 6, 10], 'class_deg': 6, 'class_size': 4, 'conductor': 2166, 'isogeny_matrix': [[1, 2, 3, 6], [2, 1, 6, 3], [3, 6, 1, 2], [6, 3, 2, 1]], 'lmfdb_iso': '2166.a', 'trace_hash': 1519692049418808961}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.021309756667720654885248219247', 'prec': 107}, 'conductor': 2166, 'gens': [], 'heights': [], 'lmfdb_label': '2166.a2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.35398243099341432718406085864', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.70796486198682865436812171727522004640', 'prec': 133}, 'tamagawa_product': 8, 'torsion_generators': [[-1813, 1813, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 1], '3': [0, 0], '19': 'a'}, 'iwp0': 5, 'lmfdb_label': '2166.a2'}
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ec_torsion_growth • Show schema
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id: 109886
{'degree': 2, 'field': [-14, -1, 1], 'lmfdb_label': '2166.a2', 'torsion': [6]}
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id: 109885
{'degree': 2, 'field': [2, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 2]}
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id: 109887
{'degree': 4, 'field': [-8, 0, 5, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [12]}
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id: 109888
{'degree': 4, 'field': [258, 24, -23, -2, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 6]}
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id: 109889
{'degree': 6, 'field': [437, -399, 54, -7, 18, -3, 1], 'lmfdb_label': '2166.a2', 'torsion': [6]}
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id: 109891
{'degree': 8, 'field': [196, 0, 204, 0, 53, 0, 18, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 12]}
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id: 109890
{'degree': 8, 'field': [10827, -3772, 4234, -936, 499, -40, 18, -4, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 4]}
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id: 109893
{'degree': 12, 'field': [14977, -29658, 36495, -16210, 14820, -9138, 4937, -1806, 690, -170, 45, -6, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 6]}
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id: 109892
{'degree': 12, 'field': [15121, -25017, -4887, 16486, 87, -231, 200, -471, 159, 8, -9, -3, 1], 'lmfdb_label': '2166.a2', 'torsion': [3, 6]}
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id: 109894
{'degree': 16, 'field': [256, 0, 5910720, 0, -1941980, 0, 165624, 0, 22470, 0, -7044, 0, 763, 0, -42, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [24]}
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id: 109895
{'degree': 16, 'field': [331776, 0, 0, 0, 168192, 0, 0, 0, -3068, 0, 0, 0, -50, 0, 0, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [2, 12]}
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id: 109896
{'degree': 18, 'field': [673405056, 326099520, -245016576, -1407024, 40219200, -10370592, 7519680, -2638872, -881712, 711396, -52632, -24408, -5964, 2592, 468, -201, -33, 0, 1], 'lmfdb_label': '2166.a2', 'torsion': [18]}
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ec_localdata • Show schema
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id: 36087
{'conductor': 2166, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '2166.a2', 'prime': 2, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 1}
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id: 36088
{'conductor': 2166, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '2166.a2', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 36089
{'conductor': 2166, 'conductor_valuation': 2, 'discriminant_valuation': 12, 'j_denominator_valuation': 6, 'kodaira_symbol': -10, 'lmfdb_label': '2166.a2', 'prime': 19, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1678051
{'adelic_gens': [[11, 2, 406, 447], [305, 12, 82, 73], [359, 444, 330, 383], [210, 145, 437, 362], [1, 0, 12, 1], [1, 6, 6, 37], [1, 12, 0, 1], [445, 12, 444, 13], [10, 3, 201, 448]], 'adelic_image': '456.96.1.?', 'conductor': 2166, 'lmfdb_label': '2166.a2', 'prime': 0}
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id: 10623
{'conductor': 2166, 'elladic_image': '8.6.0.5', 'lmfdb_label': '2166.a2', 'modell_image': '2B', 'prime': 2}
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id: 10624
{'conductor': 2166, 'elladic_image': '3.4.0.1', 'lmfdb_label': '2166.a2', 'modell_image': '3B', 'prime': 3}
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lmfdb_iso 2166.a does not appear in ec_padic