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ec_curvedata • Show schema
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{'Ciso': '15a', 'Clabel': '15a4', 'Cnumber': 4, 'abc_quality': 1.0558519748642754, 'absD': 3515625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 1, 1, 35, -28], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 15, 'degree': 2, 'elladic_images': ['8.96.0.99'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436435', 'prec': 110}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 0, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '15.a', 'lmfdb_label': '15.a8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.24.0-4.d.1.1', '8.96.0-8.n.2.5', '24.192.1-24.cv.2.2', '80.192.1.?', '160.384.5.?', '240.384.5.?', '480.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': True, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436435', 'prec': 110}, 'szpiro_ratio': 8.226531754162185, 'torsion': 8, 'torsion_primes': [2], 'torsion_structure': [8]}
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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': '1.1178508563087645508833713911', 'prec': 100}, 'conductor': 15, 'gens': [], 'heights': [], 'lmfdb_label': '15.a8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4006030423326020231801808368', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '0.35015076058315050579504520920239987269', 'prec': 133}, 'tamagawa_product': 16, 'torsion_generators': [[2, 6, 1]], 'xcoord_integral_points': [2, 7, 32]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [0, 2], '3': [0, 0], '5': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '15.a8'}
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ec_torsion_growth • Show schema
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id: 165
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [2, 8]}
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id: 167
{'degree': 4, 'field': [-9, 0, -3, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [16]}
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id: 166
{'degree': 4, 'field': [9, 0, 0, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [4, 8]}
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id: 170
{'degree': 8, 'field': [-1, 4, -4, -1, 4, -7, 7, -4, 1], 'lmfdb_label': '15.a8', 'torsion': [24]}
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id: 169
{'degree': 8, 'field': [1, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [2, 16]}
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id: 168
{'degree': 8, 'field': [25, -50, 50, -30, 14, -6, 2, -2, 1], 'lmfdb_label': '15.a8', 'torsion': [2, 16]}
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id: 175
{'degree': 16, 'field': [1, 0, 8, 0, 16, 0, -9, 0, -24, 0, 9, 0, 1, 0, 2, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [2, 24]}
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id: 172
{'degree': 16, 'field': [25, -200, 490, 0, -1134, 568, 930, -780, 451, -860, 766, -220, -24, 0, 20, -8, 1], 'lmfdb_label': '15.a8', 'torsion': [4, 16]}
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id: 171
{'degree': 16, 'field': [81, 0, 0, 0, 0, 0, 0, 0, -9, 0, 0, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [8, 8]}
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id: 174
{'degree': 16, 'field': [81, 0, 0, 0, 351, 0, 0, 0, -144, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [32]}
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id: 173
{'degree': 16, 'field': [1296, 0, 0, 0, -864, 0, 0, 0, 2241, 0, 0, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '15.a8', 'torsion': [4, 16]}
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ec_localdata • Show schema
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id: 21
{'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '15.a8', 'prime': 3, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 22
{'conductor': 15, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '15.a8', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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ec_galrep • Show schema
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id: 1665904
{'adelic_gens': [[7, 16, 375, 313], [97, 8, 0, 1], [449, 32, 448, 33], [1, 0, 32, 1], [1, 32, 4, 129], [185, 32, 182, 9], [13, 16, 254, 345], [25, 16, 184, 329], [1, 32, 0, 1]], 'adelic_image': '480.768.13.?', 'conductor': 15, 'lmfdb_label': '15.a8', 'prime': 0}
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id: 22
{'conductor': 15, 'elladic_image': '8.96.0.99', 'lmfdb_label': '15.a8', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 15.a does not appear in ec_padic