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ec_curvedata • Show schema
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{'Ciso': '4025a', 'Clabel': '4025a3', 'Cnumber': 3, 'abc_quality': 0.9409177022052051, 'absD': 862859375, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 6440, 'ainvs': [1, -1, 0, -3092, 66941], 'analytic_rank': 0, 'bad_primes': [5, 7, 23], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4025, 'degree': 2560, 'elladic_images': ['4.6.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.69908510902360492517159946386', 'prec': 103}, 'faltings_index': 3, 'faltings_ratio': 4, 'iso_nlabel': 4, 'isogeny_degrees': [1, 2, 4], 'jinv': [209267191953, 55223], 'lmfdb_iso': '4025.e', 'lmfdb_label': '4025.e1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, -1, 1, -124, 560], 'min_quad_twist_disc': 5, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '20.12.0-4.c.1.2', '56.12.0.z.1', '92.12.0.?', '280.24.0.?', '460.24.0.?', '1288.24.0.?', '6440.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, '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': '-0.10563384719344526212878020275', 'prec': 107}, 'szpiro_ratio': 4.303891478397279, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [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': '0.24704859568363602051016381465', 'prec': 103}, 'conductor': 4025, 'gens': [], 'heights': [], 'lmfdb_label': '4025.e1', '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': 4, 'torsion_generators': [[131, -131, 2]], 'xcoord_integral_points': []}
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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.e1'}
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ec_torsion_growth • Show schema
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id: 209067
{'degree': 2, 'field': [-115, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [4]}
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id: 209066
{'degree': 2, 'field': [-23, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 2]}
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id: 209068
{'degree': 2, 'field': [-1, -1, 1], 'lmfdb_label': '4025.e1', 'torsion': [4]}
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id: 209069
{'degree': 4, 'field': [461, 48, -47, -2, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 4]}
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id: 209070
{'degree': 8, 'field': [4, 0, 1880, 0, 104, 0, 20, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 4]}
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id: 209072
{'degree': 8, 'field': [151, 10, 22, -52, 43, -12, 8, -2, 1], 'lmfdb_label': '4025.e1', 'torsion': [8]}
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id: 209071
{'degree': 8, 'field': [289, 0, -86216, 0, 13422, 0, -232, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [8]}
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id: 209073
{'degree': 8, 'field': [1059, -1806, 699, -441, 240, -42, 21, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [6]}
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id: 209079
{'degree': 16, 'field': [9, 0, -135, 0, 351, 0, -270, 0, -105, 0, 270, 0, -42, 0, 0, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [12]}
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id: 209075
{'degree': 16, 'field': [5776, -12464, 48008, -85400, 160640, -167788, 175870, -120406, 81347, -36964, 17095, -4962, 1638, -290, 69, -6, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 8]}
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id: 209074
{'degree': 16, 'field': [136161, 0, 442440, 0, 69610, 0, -30492, 0, 3323, 0, 420, 0, -34, 0, 12, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [4, 4]}
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id: 209078
{'degree': 16, 'field': [7687521, 132406974, 105865137, 25211088, 9151506, -14062734, 727839, -1653246, 468015, -107016, 31458, -3612, 852, -84, 42, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [12]}
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id: 209076
{'degree': 16, 'field': [73776809, 1386509576, -377344424, -1778882488, 313556334, 628430968, -108147148, -80816400, 12818815, 4673640, -688372, -129904, 17950, 1680, -220, -8, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 8]}
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id: 209077
{'degree': 16, 'field': [550444189, 335578026, 162060692, 81014976, 19651489, 9854460, 3898757, 499968, -91736, -20076, -1363, -1680, -206, -84, -4, 0, 1], 'lmfdb_label': '4025.e1', 'torsion': [2, 6]}
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ec_localdata • Show schema
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id: 75133
{'conductor': 4025, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4025.e1', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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id: 75134
{'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 4, 'j_denominator_valuation': 4, 'kodaira_symbol': 8, 'lmfdb_label': '4025.e1', 'prime': 7, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 75135
{'conductor': 4025, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4025.e1', 'prime': 23, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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ec_galrep • Show schema
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id: 1690089
{'adelic_gens': [[1131, 1130, 5970, 171], [3536, 5155, 1405, 3866], [1, 0, 8, 1], [1, 8, 0, 1], [1, 4, 4, 17], [3863, 0, 0, 6439], [6433, 8, 6432, 9], [2416, 4355, 4995, 3736], [7, 6, 6434, 6435], [2761, 5160, 740, 1321]], 'adelic_image': '6440.48.0.?', 'conductor': 4025, 'lmfdb_label': '4025.e1', 'prime': 0}
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id: 19890
{'conductor': 4025, 'elladic_image': '4.6.0.1', 'lmfdb_label': '4025.e1', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 4025.e does not appear in ec_padic