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ec_curvedata • Show schema
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{'Ciso': '15a', 'Clabel': '15a6', 'Cnumber': 6, 'abc_quality': 1.0594919023465201, 'absD': 215233605, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, -110, -880], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 4, 'elladic_images': ['16.96.0.153'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'faltings_index': 6, 'faltings_ratio': 16, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8, 16], 'jinv': [-147281603041, 215233605], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -110, -880], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.2', '8.48.0-8.ba.2.6', '16.96.0-16.u.2.3', '20.24.0-20.h.1.1', '40.96.0-40.bm.2.4', '80.384.5.?', '96.192.1.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 0, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.29086960847710152197363562429', 'prec': 103}, 'szpiro_ratio': 9.961250033812139, '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, 1, 1, 0, 3, 1, -1, -4, 1, -2, 0, -1, -1, 2, -1, 4, -1], 'aplist': [-1, -1, 1, 0, -4, -2, 2, 4, 0, -2, 0, -10, 10, 4, 8, -10, -4, -2, 12, -8, 10, 0, 12, -6, 2], 'class_deg': 16, 'class_size': 8, 'conductor': 15, 'isogeny_matrix': [[1, 2, 4, 16, 4, 8, 16, 8], [2, 1, 2, 8, 2, 4, 8, 4], [4, 2, 1, 16, 4, 8, 16, 8], [16, 8, 16, 1, 4, 2, 4, 8], [4, 2, 4, 4, 1, 2, 4, 2], [8, 4, 8, 2, 2, 1, 2, 4], [16, 8, 16, 4, 4, 2, 1, 8], [8, 4, 8, 8, 2, 4, 8, 1]], 'lmfdb_iso': '15.a', 'trace_hash': 750292609497685491}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.55892542815438227544168569553', 'prec': 103}, 'conductor': 15, 'gens': [], 'heights': [], 'lmfdb_label': '15.a3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.70030152116630101159009041841', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35015076058315050579504520920239987269', 'prec': 133}, 'tamagawa_product': 2, 'torsion_generators': [[51, -55, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 3], '3': [0, 0], '5': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '15.a3'}
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ec_torsion_growth • Show schema
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id: 201
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '15.a3', 'torsion': [4]}
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id: 202
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [4]}
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id: 200
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 2]}
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id: 205
{'degree': 4, 'field': [-5, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [8]}
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id: 206
{'degree': 4, 'field': [1, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [8]}
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id: 203
{'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 4]}
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id: 204
{'degree': 4, 'field': [5, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 4]}
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id: 207
{'degree': 4, 'field': [25, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [8]}
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id: 211
{'degree': 8, 'field': [-5, 0, 0, 0, -5, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [16]}
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id: 215
{'degree': 8, 'field': [-1, 4, -4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '15.a3', 'torsion': [6]}
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id: 210
{'degree': 8, 'field': [1, 0, 0, 0, 7, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 8]}
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id: 209
{'degree': 8, 'field': [1, 2, 2, -10, 11, -10, 8, -4, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 8]}
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id: 212
{'degree': 8, 'field': [25, 0, 0, 0, -8, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [16]}
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id: 208
{'degree': 8, 'field': [36, 0, -56, 0, 16, 0, 4, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [4, 4]}
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id: 214
{'degree': 8, 'field': [625, 0, 0, 0, -40, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [16]}
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id: 213
{'degree': 8, 'field': [625, 0, 0, 0, 40, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [16]}
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id: 217
{'degree': 16, 'field': [1, 0, 0, 0, -36, 0, 0, 0, 646, 0, 0, 0, -36, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [4, 8]}
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id: 220
{'degree': 16, 'field': [1, 0, 0, 0, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 16]}
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id: 223
{'degree': 16, 'field': [1, 0, 8, 0, 16, 0, -9, 0, -24, 0, 9, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [12]}
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id: 218
{'degree': 16, 'field': [1, 0, 668, 0, -742, 0, 156, 0, -85, 0, 36, 0, 38, 0, 8, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 16]}
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id: 222
{'degree': 16, 'field': [9, 0, -63, 0, 135, 0, -146, 0, 125, 0, -89, 0, 43, 0, -10, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [12]}
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id: 216
{'degree': 16, 'field': [25, 0, 0, 0, 0, 0, 0, 0, 235, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [4, 8]}
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id: 219
{'degree': 16, 'field': [625, 0, 0, 0, 0, 0, 0, 0, 175, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 16]}
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id: 221
{'degree': 16, 'field': [625, 0, 1000, 0, 400, 0, 1875, 0, 600, 0, 165, 0, 25, 0, 10, 0, 1], 'lmfdb_label': '15.a3', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 25
{'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 16, 'j_denominator_valuation': 16, 'kodaira_symbol': 20, 'lmfdb_label': '15.a3', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 26
{'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '15.a3', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1665899
{'adelic_gens': [[449, 32, 448, 33], [1, 0, 32, 1], [23, 18, 318, 395], [161, 32, 176, 33], [5, 28, 68, 381], [421, 32, 436, 33], [60, 31, 239, 324], [1, 32, 0, 1], [214, 3, 365, 268]], 'adelic_image': '480.768.13.?', 'conductor': 15, 'lmfdb_label': '15.a3', 'prime': 0}
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id: 17
{'conductor': 15, 'elladic_image': '16.96.0.153', 'lmfdb_label': '15.a3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 15.a does not appear in ec_padic