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ec_curvedata • Show schema
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{'Ciso': '4025a', 'Clabel': '4025a2', 'Cnumber': 2, 'abc_quality': 0.9262544492890874, 'absD': 405015625, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 3220, 'ainvs': [1, -1, 0, -217, 816], 'analytic_rank': 0, 'bad_primes': [5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4025, 'degree': 1280, 'elladic_images': ['2.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.35251151874363227046298340313', 'prec': 103}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2], 'jinv': [72511713, 25921], 'lmfdb_iso': '4025.e', 'lmfdb_label': '4025.e2', 'lmfdb_number': 2, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -9, 8], 'min_quad_twist_disc': 5, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '20.12.0-2.a.1.1', '28.12.0.b.1', '92.12.0.?', '140.24.0.?', '460.24.0.?', '644.24.0.?', '3220.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 0, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.45220743747341791683739626348', 'prec': 107}, 'szpiro_ratio': 3.343969782361491, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 1, 0, -1, 0, 0, -1, -3, -3, 0, 4, 0, -6, -1, 0, -1, 2, -3, 4, 0], 'aplist': [1, 0, 0, -1, 4, -6, 2, 4, 1, -2, -4, 2, -6, -12, 12, 10, 0, 2, -12, 8, 14, 8, 4, 6, 10], 'class_deg': 4, 'class_size': 4, 'conductor': 4025, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4025.e', 'trace_hash': 440634469277035009}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.49409719136727204102032762930', 'prec': 103}, 'conductor': 4025, 'gens': [], 'heights': [], 'lmfdb_label': '4025.e2', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.5434849664317647729080856969', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '1.5434849664317647729080856969377655934', 'prec': 130}, 'tamagawa_product': 16, 'torsion_generators': [[-16, 8, 1], [4, -2, 1]], 'xcoord_integral_points': [-16, 4]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [4, 0], '5': 'a', '7': [0, 0], '23': [1, 0]}, 'iwp0': 3, 'lmfdb_label': '4025.e2'}
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ec_torsion_growth • Show schema
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id: 209058
{'degree': 4, 'field': [4, 2, 5, -1, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 4]}
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id: 209060
{'degree': 4, 'field': [49, 0, -9, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 4]}
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id: 209059
{'degree': 4, 'field': [400, 0, -75, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 4]}
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id: 209061
{'degree': 8, 'field': [1059, -1806, 699, -441, 240, -42, 21, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 6]}
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id: 209063
{'degree': 16, 'field': [1, 0, -12, 0, 107, 0, -228, 0, 328, 0, -228, 0, 107, 0, -12, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 8]}
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id: 209064
{'degree': 16, 'field': [256, 0, -11520, 0, 58128, 0, -423360, 0, 450968, 0, -105840, 0, 3633, 0, -180, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 8]}
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id: 209062
{'degree': 16, 'field': [13456, 0, 21596, 0, 498297, 0, -316220, 0, 112876, 0, -18710, 0, 1572, 0, -64, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [4, 4]}
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id: 209065
{'degree': 16, 'field': [519841, 0, 1558772, 0, 1165862, 0, 373588, 0, 62083, 0, 6148, 0, 482, 0, 32, 0, 1], 'lmfdb_label': '4025.e2', 'torsion': [2, 8]}
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ec_localdata • Show schema
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id: 75130
{'conductor': 4025, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4025.e2', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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id: 75131
{'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4025.e2', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 75132
{'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4025.e2', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1690090
{'adelic_gens': [[1, 0, 4, 1], [281, 1290, 0, 1], [2901, 1290, 1280, 2571], [1, 4, 0, 1], [643, 0, 0, 3219], [2761, 2580, 370, 1941], [3217, 4, 3216, 5]], 'adelic_image': '3220.48.0.?', 'conductor': 4025, 'lmfdb_label': '4025.e2', 'prime': 0}
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id: 19891
{'conductor': 4025, 'elladic_image': '2.6.0.1', 'lmfdb_label': '4025.e2', 'modell_image': '2Cs', 'prime': 2}
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lmfdb_iso 4025.e does not appear in ec_padic