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ec_curvedata • Show schema
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{'Ciso': '4800x', 'Clabel': '4800x1', 'Cnumber': 1, 'abc_quality': 1.027047455683347, 'absD': 3000000, 'adelic_genus': 0, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -108, -462], 'analytic_rank': 0, 'bad_primes': [2, 3, 5], 'class_deg': 4, 'class_size': 4, 'cm': 0, 'conductor': 4800, 'degree': 1024, 'elladic_images': ['8.12.0.11'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.031924995433911384206148844095', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 66, 'isogeny_degrees': [1, 2, 4], 'jinv': [140608, 3], 'lmfdb_iso': '4800.co', 'lmfdb_label': '4800.co3', 'lmfdb_number': 3, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -17, 33], 'min_quad_twist_disc': -40, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.6.0.c.1', '8.12.0.m.1', '12.12.0.h.1', '24.24.0.bk.1', '40.24.0-8.m.1.2', '120.48.0.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 1, 'optimality': 1, 'potential_good_reduction': False, 'rank': 0, 'regulator': 1, 'semistable': False, 'sha': 4, 'sha_primes': [2], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1193675510631114578028468832', 'prec': 103}, 'szpiro_ratio': 3.02832911837421, 'torsion': 2, 'torsion_primes': [2], 'torsion_structure': [2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, 4, 0, 1, 0, -4, 0, -2, 0, 0, 0, 6, 0, 4, 0], 'aplist': [0, 1, 0, 4, -4, -2, 6, 4, 0, -2, 4, -2, 2, 4, -8, 10, 4, -6, 4, -16, 6, 4, 12, 10, 14], 'class_deg': 4, 'class_size': 4, 'conductor': 4800, 'isogeny_matrix': [[1, 2, 4, 4], [2, 1, 2, 2], [4, 2, 1, 4], [4, 2, 4, 1]], 'lmfdb_iso': '4800.co', 'trace_hash': 2279384013327162677}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.93814571940105592902819779771', 'prec': 103}, 'conductor': 4800, 'gens': [], 'heights': [], 'lmfdb_label': '4800.co3', 'ngens': 0, 'rank_bounds': [0, 0], 'real_period': {'__RealLiteral__': 0, 'data': '1.4817422251079573669211297255', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '4.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.9634844502159147338422594510495868552', 'prec': 130}, 'tamagawa_product': 2, 'torsion_generators': [[-7, 0, 1]], 'xcoord_integral_points': [-7]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [3, 0], '5': 'a'}, 'iwp0': 3, 'lmfdb_label': '4800.co3'}
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ec_torsion_growth • Show schema
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id: 249489
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 2]}
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id: 249490
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [4]}
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id: 249491
{'degree': 2, 'field': [30, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [4]}
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id: 249492
{'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 4]}
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id: 249496
{'degree': 8, 'field': [-1875, 0, 2000, 0, -150, 0, 0, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [6]}
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id: 249493
{'degree': 8, 'field': [4, 0, -88, 0, 60, 0, -16, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 4]}
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id: 249494
{'degree': 8, 'field': [9, 0, -18, 0, 25, 0, -6, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [8]}
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id: 249495
{'degree': 8, 'field': [3364, 0, 944, 0, 132, 0, 8, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [8]}
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id: 249497
{'degree': 16, 'field': [16, 0, -352, 0, 7504, 0, -5152, 0, 2188, 0, -784, 0, 196, 0, -16, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [4, 4]}
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id: 249499
{'degree': 16, 'field': [121, -924, 2300, -1140, -976, 1656, -24, -540, 521, 96, -180, 108, 98, -12, -16, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 8]}
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id: 249498
{'degree': 16, 'field': [4174, -5824, 9156, -8024, 7758, -5520, 3748, -2132, 1359, -844, 424, -108, 18, -28, 24, -8, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 8]}
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id: 249501
{'degree': 16, 'field': [92161, -70844, 21860, 50428, -36498, 16792, 1944, -1172, 1384, -724, 996, -532, 246, -64, 20, -4, 1], 'lmfdb_label': '4800.co3', 'torsion': [12]}
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id: 249500
{'degree': 16, 'field': [390625, 0, 312500, 0, -218750, 0, -200000, 0, -60625, 0, -8000, 0, -350, 0, 20, 0, 1], 'lmfdb_label': '4800.co3', 'torsion': [2, 6]}
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id: 249502
{'degree': 16, 'field': [18586809, 22614516, 9566688, 151548, -1376898, -521520, -73620, -17100, 1024, 6524, 2008, -20, -58, 16, -8, -4, 1], 'lmfdb_label': '4800.co3', 'torsion': [12]}
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ec_localdata • Show schema
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id: 92002
{'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '4800.co3', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 92003
{'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4800.co3', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 92004
{'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '4800.co3', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 2}
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ec_galrep • Show schema
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id: 1695221
{'adelic_gens': [[113, 8, 112, 9], [7, 6, 114, 115], [16, 35, 75, 76], [1, 0, 8, 1], [109, 90, 70, 109], [1, 4, 4, 17], [116, 25, 55, 6], [23, 0, 0, 119], [1, 8, 0, 1]], 'adelic_image': '120.48.0.?', 'conductor': 4800, 'lmfdb_label': '4800.co3', 'prime': 0}
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id: 23741
{'conductor': 4800, 'elladic_image': '8.12.0.11', 'lmfdb_label': '4800.co3', 'modell_image': '2B', 'prime': 2}
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lmfdb_iso 4800.co does not appear in ec_padic