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ec_curvedata • Show schema
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{'Ciso': '120a', 'Clabel': '120a1', 'Cnumber': 1, 'abc_quality': 0.9923662209495213, 'absD': 720, 'adelic_genus': 1, 'adelic_index': 192, 'adelic_level': 240, 'ainvs': [0, 1, 0, -15, 18], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 8, 'class_size': 6, 'cm': 0, 'conductor': 120, 'degree': 8, 'elladic_images': ['16.48.0.30'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.55972190577000337273713211445', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [24918016, 45], 'lmfdb_iso': '120.b', 'lmfdb_label': '120.b5', 'lmfdb_number': 5, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, 1, 0, -15, 18], 'min_quad_twist_disc': 1, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0-4.c.1.1', '8.24.0-8.n.1.2', '10.6.0.a.1', '16.48.0-16.f.2.3', '20.24.0-20.g.1.2', '24.48.0-24.by.2.3', '40.48.0-40.bj.1.8', '48.96.0-48.bq.1.7', '80.96.0.?', '120.96.0.?', '240.192.1.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 3, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.79077096595665180920954282160', 'prec': 107}, 'szpiro_ratio': 4.136548201058319, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [4]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 1, 0, 0, 0, 1, 0, -4, 0, 6, 0, 1, 0, -6, 0, -4, 0], 'aplist': [0, 1, 1, 0, -4, 6, -6, -4, 0, -2, -8, -2, -6, 12, 8, 6, 12, 14, 4, 8, -6, -8, -12, 10, 2], 'class_deg': 8, 'class_size': 6, 'conductor': 120, 'isogeny_matrix': [[1, 2, 4, 4, 8, 8], [2, 1, 2, 2, 4, 4], [4, 2, 1, 4, 8, 8], [4, 2, 4, 1, 2, 2], [8, 4, 8, 2, 1, 4], [8, 4, 8, 2, 4, 1]], 'lmfdb_iso': '120.b', 'trace_hash': 704992717552055982}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '3.0631500407152797643350432787', 'prec': 100}, 'conductor': 120, 'gens': [], 'heights': [], 'lmfdb_label': '120.b5', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '5.0779771118533319593856257082', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.2694942779633329898464064270624422458', 'prec': 130}, 'tamagawa_product': 4, 'torsion_generators': [[3, 3, 1]], 'xcoord_integral_points': [2, 3]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '120.b5'}
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ec_torsion_growth • Show schema
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id: 4476
{'degree': 2, 'field': [-15, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [8]}
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id: 4475
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [8]}
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id: 4474
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 4]}
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id: 4477
{'degree': 4, 'field': [1, 8, -7, -2, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 8]}
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id: 4481
{'degree': 8, 'field': [-54, 0, 504, 720, 246, -60, -36, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [16]}
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id: 4482
{'degree': 8, 'field': [-3, 0, -28, 0, -6, 0, 0, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [12]}
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id: 4479
{'degree': 8, 'field': [1, 2, 2, -10, 11, -10, 8, -4, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 8]}
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id: 4480
{'degree': 8, 'field': [97, -108, 116, -72, 24, -12, 8, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [16]}
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id: 4478
{'degree': 8, 'field': [121, 22, 2, -50, 31, -10, 8, -4, 1], 'lmfdb_label': '120.b5', 'torsion': [4, 4]}
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id: 4486
{'degree': 16, 'field': [-284, -3280, 16416, -3152, -46068, 19896, 44752, -21800, -18558, 10112, 3328, -2232, -174, 224, -12, -8, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 16]}
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id: 4488
{'degree': 16, 'field': [-138, 492, -384, 660, -1038, -468, 298, 28, 1712, 228, -790, 38, 90, -4, -4, -4, 1], 'lmfdb_label': '120.b5', 'torsion': [24]}
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id: 4483
{'degree': 16, 'field': [1, 2, 2, 24, 13, -74, 114, -58, -12, 44, -24, -2, 13, -12, 8, -4, 1], 'lmfdb_label': '120.b5', 'torsion': [4, 8]}
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id: 4487
{'degree': 16, 'field': [9, 0, 5832, 0, -5570, 0, 1584, 0, -105, 0, 96, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 12]}
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id: 4484
{'degree': 16, 'field': [2025, 0, 0, 0, -1350, 0, 0, 0, 415, 0, 0, 0, -30, 0, 0, 0, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 16]}
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id: 4489
{'degree': 16, 'field': [3481, -708, -20966, -2748, 36070, 3450, -32918, -13674, 3628, 5580, 1048, -1416, -134, 198, -20, -6, 1], 'lmfdb_label': '120.b5', 'torsion': [24]}
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id: 4485
{'degree': 16, 'field': [5881, -10024, 15096, -19436, 22914, -20220, 14080, -7772, 3777, -1612, 700, -348, 204, -100, 36, -8, 1], 'lmfdb_label': '120.b5', 'torsion': [2, 16]}
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ec_localdata • Show schema
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id: 799
{'conductor': 120, 'conductor_valuation': 3, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 3, 'lmfdb_label': '120.b5', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 800
{'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '120.b5', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 801
{'conductor': 120, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '120.b5', 'prime': 5, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1666252
{'adelic_gens': [[5, 4, 236, 237], [1, 16, 180, 181], [173, 16, 64, 165], [112, 5, 195, 226], [225, 16, 224, 17], [1, 0, 16, 1], [15, 2, 142, 227], [1, 16, 0, 1], [45, 16, 74, 59]], 'adelic_image': '240.192.1.?', 'conductor': 120, 'lmfdb_label': '120.b5', 'prime': 0}
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id: 440
{'conductor': 120, 'elladic_image': '16.48.0.30', 'lmfdb_label': '120.b5', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 120.b does not appear in ec_padic