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ec_curvedata • Show schema
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{'Ciso': '75b', 'Clabel': '75b6', 'Cnumber': 6, 'abc_quality': 1.0558519748642754, 'absD': 54931640625, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 480, 'ainvs': [1, 0, 1, 874, -5227], 'analytic_rank': 0, 'bad_primes': [3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 75, 'degree': 48, 'elladic_images': ['16.96.0.197'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.74901497441417905456539923018', 'prec': 103}, 'faltings_index': 4, 'faltings_ratio': 8, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [4733169839, 3515625], 'lmfdb_iso': '75.b', 'lmfdb_label': '75.b8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, 35, -28], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0.n.2', '16.96.0-8.n.2.2', '20.24.0-4.d.1.1', '24.96.1.cv.2', '40.96.0-8.n.2.3', '48.192.1-24.cv.2.4', '80.192.1.?', '120.192.1.?', '160.384.5.?', '240.384.5.?', '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': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.055703981802871132734980436433', 'prec': 110}, 'szpiro_ratio': 7.396543454448738, '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, 0, -3, 1, 0, -4, -1, 2, 0, 0, -1, -2, 1, 4, 0], 'aplist': [1, 1, 0, 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': 75, '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': '75.b', 'trace_hash': 1988189362737059693}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.22357017126175291017667427821', 'prec': 103}, 'conductor': 75, 'gens': [], 'heights': [], 'lmfdb_label': '75.b8', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '0.62636872242974274728715805032', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2527374448594854945743161006323838319', 'prec': 130}, 'tamagawa_product': 8, 'torsion_generators': [[23, -27, 2]], 'xcoord_integral_points': []}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [1, 2], '3': [1, 0], '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '75.b8'}
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ec_torsion_growth • Show schema
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id: 2687
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '75.b8', 'torsion': [8]}
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id: 2686
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [2, 2]}
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id: 2688
{'degree': 2, 'field': [5, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [4]}
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id: 2692
{'degree': 4, 'field': [-9, 0, -3, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [16]}
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id: 2689
{'degree': 4, 'field': [1, 0, 3, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [2, 8]}
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id: 2690
{'degree': 4, 'field': [81, 0, -12, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [8]}
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id: 2691
{'degree': 4, 'field': [81, 0, 12, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [8]}
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id: 2694
{'degree': 8, 'field': [1, 0, 0, 0, 3, 0, 0, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [2, 16]}
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id: 2696
{'degree': 8, 'field': [9, -9, -15, 3, 15, -2, -3, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [6]}
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id: 2695
{'degree': 8, 'field': [25, -50, 50, -30, 14, -6, 2, -2, 1], 'lmfdb_label': '75.b8', 'torsion': [2, 16]}
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id: 2693
{'degree': 8, 'field': [145, -140, 164, -44, 13, 8, 2, -4, 1], 'lmfdb_label': '75.b8', 'torsion': [4, 8]}
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id: 2702
{'degree': 16, 'field': [9, 0, -63, 0, 135, 0, -146, 0, 125, 0, -89, 0, 43, 0, -10, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [24]}
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id: 2703
{'degree': 16, 'field': [9, 0, 63, 0, 135, 0, 146, 0, 125, 0, 89, 0, 43, 0, 10, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [12]}
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id: 2697
{'degree': 16, 'field': [25, -200, 490, 0, -1134, 568, 930, -780, 451, -860, 766, -220, -24, 0, 20, -8, 1], 'lmfdb_label': '75.b8', 'torsion': [4, 16]}
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id: 2700
{'degree': 16, 'field': [81, 0, 0, 0, 351, 0, 0, 0, -144, 0, 0, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [32]}
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id: 2701
{'degree': 16, 'field': [81, 0, 351, 0, 549, 0, 549, 0, 345, 0, 124, 0, 39, 0, 6, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [2, 6]}
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id: 2698
{'degree': 16, 'field': [2916, 0, 7776, 0, 14796, 0, 7776, 0, 1269, 0, -216, 0, -72, 0, 0, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [16]}
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id: 2699
{'degree': 16, 'field': [6561, 0, -11664, 0, 11772, 0, -8640, 0, 4671, 0, -1440, 0, 252, 0, -24, 0, 1], 'lmfdb_label': '75.b8', 'torsion': [16]}
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ec_localdata • Show schema
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id: 418
{'conductor': 75, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '75.b8', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 419
{'conductor': 75, 'conductor_valuation': 2, 'discriminant_valuation': 14, 'j_denominator_valuation': 8, 'kodaira_symbol': -12, 'lmfdb_label': '75.b8', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1666082
{'adelic_gens': [[7, 16, 375, 313], [449, 32, 448, 33], [1, 0, 32, 1], [1, 32, 4, 129], [185, 32, 182, 9], [383, 472, 0, 479], [13, 16, 254, 345], [25, 16, 184, 329], [1, 32, 0, 1]], 'adelic_image': '480.768.13.?', 'conductor': 75, 'lmfdb_label': '75.b8', 'prime': 0}
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id: 240
{'conductor': 75, 'elladic_image': '16.96.0.197', 'lmfdb_label': '75.b8', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 75.b does not appear in ec_padic