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ec_curvedata • Show schema
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{'Ciso': '4800cd', 'Clabel': '4800cd2', 'Cnumber': 2, 'abc_quality': 0.9622954410890624, 'absD': 921600000000, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 240, 'ainvs': [0, 1, 0, -8033, -275937], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 4800, 'degree': 6144, 'elladic_images': ['16.96.0.69'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.0955885646941517092740152909', 'prec': 100}, 'faltings_index': 1, 'faltings_ratio': 2, 'iso_nlabel': 51, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [13997521, 225], 'lmfdb_iso': '4800.bz', 'lmfdb_label': '4800.bz6', 'lmfdb_number': 6, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 1, 1, -5, 2], 'min_quad_twist_disc': -40, 'modell_images': ['2Cs'], 'modm_images': ['2.6.0.a.1', '4.12.0.b.1', '8.48.0-8.i.1.1', '16.96.0-16.d.2.11', '24.96.0-24.bb.2.9', '40.96.0-40.bd.1.2', '48.192.1-48.n.1.11', '60.24.0.c.1', '80.384.5.?', '120.192.1.?', '240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 5, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '4.2977837449033302599224784821', 'prec': 100}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': 1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-0.74885116236281644215221255790', 'prec': 107}, 'szpiro_ratio': 4.552380568147635, 'torsion': 4, 'torsion_primes': [2], 'torsion_structure': [2, 2]}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, -4, 0, -2, 0, 0, 0, -2, 0, 4, 0], 'aplist': [0, 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': 4800, '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': '4800.bz', 'trace_hash': 1211258731738643039}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.11178508563087645508833713911', 'prec': 103}, 'conductor': 4800, 'gens': [[967, 29952, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '4.2977837449033302599224784821', 'prec': 100}], 'lmfdb_label': '4800.bz6', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.50477611192648707691714473191', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.3388371373063204371795878507884350707', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-47, 0, 1], [103, 0, 1]], 'xcoord_integral_points': [-57, -47, 103, 967]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [1, 1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 1, 0], '29': [1, 0], '31': [1, 1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4800.bz6'}
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ec_torsion_growth • Show schema
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id: 250494
{'degree': 2, 'field': [10, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 4]}
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id: 250496
{'degree': 4, 'field': [1, 0, -8, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 4]}
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id: 250497
{'degree': 4, 'field': [4, 0, 6, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 8]}
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id: 250495
{'degree': 4, 'field': [16, 0, -2, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 4]}
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id: 250503
{'degree': 8, 'field': [-1200, 0, -3160, 0, 120, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 6]}
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id: 250499
{'degree': 8, 'field': [1, 0, -4, 0, -9, 0, -4, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 8]}
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id: 250498
{'degree': 8, 'field': [16, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [4, 4]}
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id: 250502
{'degree': 8, 'field': [241, -124, 124, -58, 24, 4, 1, -2, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 16]}
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id: 250500
{'degree': 8, 'field': [256, 0, -136, 0, 81, 0, -16, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 8]}
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id: 250501
{'degree': 8, 'field': [625, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 8]}
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id: 250504
{'degree': 16, 'field': [1, 0, 0, 0, -7, 0, 0, 0, 48, 0, 0, 0, -7, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [4, 8]}
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id: 250507
{'degree': 16, 'field': [1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 16]}
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id: 250505
{'degree': 16, 'field': [225, 0, 900, 0, 870, 0, 660, 0, 451, 0, 196, 0, 66, 0, 16, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [4, 8]}
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id: 250506
{'degree': 16, 'field': [256, 0, 0, 0, 16, 0, 0, 0, 216, 0, 0, 0, 1, 0, 0, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [4, 8]}
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id: 250508
{'degree': 16, 'field': [160000, 0, 128000, 0, 25600, 0, 60000, 0, 9600, 0, 1320, 0, 100, 0, 20, 0, 1], 'lmfdb_label': '4800.bz6', 'torsion': [2, 12]}
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ec_localdata • Show schema
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id: 92266
{'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 18, 'j_denominator_valuation': 0, 'kodaira_symbol': -12, 'lmfdb_label': '4800.bz6', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 4}
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id: 92267
{'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '4800.bz6', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 2}
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id: 92268
{'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '4800.bz6', 'prime': 5, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 4}
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ec_galrep • Show schema
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id: 1695174
{'adelic_gens': [[1, 0, 16, 1], [179, 232, 70, 43], [161, 16, 6, 97], [1, 16, 0, 1], [1, 16, 4, 65], [225, 16, 224, 17], [235, 224, 236, 47], [225, 232, 32, 31]], 'adelic_image': '240.768.13.?', 'conductor': 4800, 'lmfdb_label': '4800.bz6', 'prime': 0}
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id: 23688
{'conductor': 4800, 'elladic_image': '16.96.0.69', 'lmfdb_label': '4800.bz6', 'modell_image': '2Cs', 'prime': 2}
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ec_padic • Show schema
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id: 174933
{'lmfdb_iso': '4800.bz', 'p': 11, 'prec': 20, 'unit': 60243483828572023142, 'val': 1}
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id: 174939
{'lmfdb_iso': '4800.bz', 'p': 13, 'prec': 20, 'unit': 145399912140028618071, 'val': 1}
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id: 174941
{'lmfdb_iso': '4800.bz', 'p': 17, 'prec': 20, 'unit': 86447417322788101936468, 'val': 1}
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id: 174942
{'lmfdb_iso': '4800.bz', 'p': 19, 'prec': 20, 'unit': 1755796605468443960767827, 'val': 1}
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id: 174938
{'lmfdb_iso': '4800.bz', 'p': 29, 'prec': 20, 'unit': 4316659388614581058176289742, 'val': 1}
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id: 174934
{'lmfdb_iso': '4800.bz', 'p': 37, 'prec': 20, 'unit': 549893009073814573999027199018, 'val': 1}
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id: 174936
{'lmfdb_iso': '4800.bz', 'p': 41, 'prec': 20, 'unit': 3723932435808031297633959935268, 'val': 1}
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id: 174937
{'lmfdb_iso': '4800.bz', 'p': 43, 'prec': 20, 'unit': 1354216653278264985145659653777, 'val': 1}
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id: 174940
{'lmfdb_iso': '4800.bz', 'p': 47, 'prec': 20, 'unit': 43157010205683798607511824228484, 'val': 1}
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id: 174943
{'lmfdb_iso': '4800.bz', 'p': 53, 'prec': 20, 'unit': 84983392135992346664191820800125, 'val': 1}
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id: 174947
{'lmfdb_iso': '4800.bz', 'p': 59, 'prec': 20, 'unit': 2213793566094885988931346855115973, 'val': 1}
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id: 174948
{'lmfdb_iso': '4800.bz', 'p': 61, 'prec': 20, 'unit': 543110047934878398977711858213688, 'val': 1}
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id: 174932
{'lmfdb_iso': '4800.bz', 'p': 67, 'prec': 20, 'unit': 15652361903037683367672562905369386, 'val': 1}
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id: 174935
{'lmfdb_iso': '4800.bz', 'p': 71, 'prec': 20, 'unit': 108153419725689655534085833482982999, 'val': 1}
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id: 174944
{'lmfdb_iso': '4800.bz', 'p': 73, 'prec': 20, 'unit': 178417821851772767681151160365561960, 'val': 1}
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id: 174945
{'lmfdb_iso': '4800.bz', 'p': 83, 'prec': 20, 'unit': 2712322136180633508787345176557956226, 'val': 1}
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id: 174946
{'lmfdb_iso': '4800.bz', 'p': 89, 'prec': 20, 'unit': 1305284119515383271454516366773802082, 'val': 1}
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id: 174931
{'lmfdb_iso': '4800.bz', 'p': 97, 'prec': 20, 'unit': 51799032339526436962490907097444675260, 'val': 1}