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ec_curvedata • Show schema
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{'Ciso': '4800bf', 'Clabel': '4800bf1', 'Cnumber': 1, 'abc_quality': 1.0439051029424253, 'absD': 120000, 'adelic_genus': 1, 'adelic_index': 48, 'adelic_level': 120, 'ainvs': [0, 1, 0, -33, -87], 'analytic_rank': 1, 'bad_primes': [2, 3, 5], 'class_deg': 5, 'class_size': 2, 'cm': 0, 'conductor': 4800, 'degree': 480, 'elladic_images': ['5.12.0.2'], 'faltings_height': {'__RealLiteral__': 0, 'data': '-0.24652474381470015997657587053', 'prec': 107}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 42, 'isogeny_degrees': [1, 5], 'jinv': [-102400, 3], 'lmfdb_iso': '4800.bq', 'lmfdb_label': '4800.bq1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 1, -8, -7], 'min_quad_twist_disc': 8, 'modell_images': ['5B.4.2'], 'modm_images': ['5.12.0.a.2', '6.2.0.a.1', '30.24.1.d.2', '40.24.0-5.a.2.4', '120.48.1.?'], 'nonmax_primes': [5], 'nonmax_rad': 5, 'num_bad_primes': 3, 'num_int_pts': 2, 'optimality': 1, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '1.3853003397069058826025615725', 'prec': 100}, 'semistable': False, 'serre_invariants': [[2, 2, 75], [3, 4, 1600], [5, 14, 192]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.1295776382393729395521117090', 'prec': 103}, 'szpiro_ratio': 2.6169998262921252, 'torsion': 1, 'torsion_primes': [], 'torsion_structure': []}
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ec_classdata • Show schema
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{'anlist': [0, 1, 0, 1, 0, 0, 0, -3, 0, 1, 0, -2, 0, -1, 0, 0, 0, 2, 0, 5, 0], 'aplist': [0, 1, 0, -3, -2, -1, 2, 5, 6, -10, -3, -2, -8, -1, 2, 4, 10, -7, 3, -8, -14, 0, -6, 0, 17], 'class_deg': 5, 'class_size': 2, 'conductor': 4800, 'isogeny_matrix': [[1, 5], [5, 1]], 'lmfdb_iso': '4800.bq', 'trace_hash': 568812346329284534}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '1.6373015455564098207950064873', 'prec': 100}, 'conductor': 4800, 'gens': [[8, 15, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '1.3853003397069058826025615725', 'prec': 100}], 'lmfdb_label': '4800.bq1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.99174550261186491375809973541', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '4.1215961450130377408767881826645568144', 'prec': 130}, 'tamagawa_product': 3, 'torsion_generators': [], 'xcoord_integral_points': [8]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [2, 0], '5': 'a', '7': [1, 0], '11': [1, 0], '13': [1, 0], '17': [1, 0], '19': [1, 0], '23': [3, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '4800.bq1'}
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ec_torsion_growth • Show schema
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id: 249711
{'degree': 3, 'field': [-3, -3, -1, 1], 'lmfdb_label': '4800.bq1', 'torsion': [2]}
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id: 249712
{'degree': 4, 'field': [20, 0, 10, 0, 1], 'lmfdb_label': '4800.bq1', 'torsion': [5]}
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id: 249713
{'degree': 6, 'field': [3, 3, -2, -3, 4, -3, 1], 'lmfdb_label': '4800.bq1', 'torsion': [2, 2]}
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id: 249714
{'degree': 8, 'field': [-48, 0, 56, 0, -24, 0, 0, 0, 1], 'lmfdb_label': '4800.bq1', 'torsion': [3]}
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id: 249715
{'degree': 10, 'field': [-640, 0, 80, 0, 200, 0, 100, 0, 10, 0, 1], 'lmfdb_label': '4800.bq1', 'torsion': [5]}
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id: 249716
{'degree': 12, 'field': [-3, 0, -20, 0, 87, 0, -100, 0, -1, 0, 0, 0, 1], 'lmfdb_label': '4800.bq1', 'torsion': [4]}
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id: 249717
{'degree': 12, 'field': [20, 0, 120, 0, 0, 0, -20, 0, 0, 0, 0, 0, 1], 'lmfdb_label': '4800.bq1', 'torsion': [10]}
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ec_localdata • Show schema
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id: 92065
{'conductor': 4800, 'conductor_valuation': 6, 'discriminant_valuation': 6, 'j_denominator_valuation': 0, 'kodaira_symbol': 2, 'lmfdb_label': '4800.bq1', 'prime': 2, 'reduction_type': 0, 'root_number': 1, 'tamagawa_number': 1}
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id: 92066
{'conductor': 4800, 'conductor_valuation': 1, 'discriminant_valuation': 1, 'j_denominator_valuation': 1, 'kodaira_symbol': 5, 'lmfdb_label': '4800.bq1', 'prime': 3, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 1}
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id: 92067
{'conductor': 4800, 'conductor_valuation': 2, 'discriminant_valuation': 4, 'j_denominator_valuation': 0, 'kodaira_symbol': 4, 'lmfdb_label': '4800.bq1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1695156
{'adelic_gens': [[3, 10, 20, 19], [31, 0, 0, 1], [111, 10, 110, 11], [1, 0, 10, 1], [6, 13, 65, 1], [114, 107, 115, 119], [109, 110, 95, 99], [59, 0, 0, 119], [21, 10, 20, 11], [1, 10, 0, 1]], 'adelic_image': '120.48.1.?', 'conductor': 4800, 'lmfdb_label': '4800.bq1', 'prime': 0}
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id: 23675
{'conductor': 4800, 'elladic_image': '5.12.0.2', 'lmfdb_label': '4800.bq1', 'modell_image': '5B.4.2', 'prime': 5}
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ec_padic • Show schema
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id: 174663
{'lmfdb_iso': '4800.bq', 'p': 7, 'prec': 20, 'unit': 6837168585581093, 'val': 1}
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id: 174661
{'lmfdb_iso': '4800.bq', 'p': 11, 'prec': 20, 'unit': 13381030511335635631, 'val': 1}
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id: 174667
{'lmfdb_iso': '4800.bq', 'p': 13, 'prec': 20, 'unit': 135223917673132405196, 'val': 1}
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id: 174669
{'lmfdb_iso': '4800.bq', 'p': 17, 'prec': 20, 'unit': 124473920053926634703329, 'val': 1}
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id: 174670
{'lmfdb_iso': '4800.bq', 'p': 19, 'prec': 20, 'unit': 776924291900694316567339, 'val': 1}
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id: 174673
{'lmfdb_iso': '4800.bq', 'p': 23, 'prec': 20, 'unit': 2114066545993385477120484, 'val': 2}
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id: 174666
{'lmfdb_iso': '4800.bq', 'p': 29, 'prec': 20, 'unit': 4531179693773101601783283037, 'val': 1}
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id: 174678
{'lmfdb_iso': '4800.bq', 'p': 31, 'prec': 20, 'unit': 7713567078325977298351399040, 'val': 1}
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id: 174662
{'lmfdb_iso': '4800.bq', 'p': 37, 'prec': 20, 'unit': 83665261859061857864501188093, 'val': 1}
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id: 174664
{'lmfdb_iso': '4800.bq', 'p': 41, 'prec': 20, 'unit': 1837881396865809237923798173813, 'val': 1}
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id: 174665
{'lmfdb_iso': '4800.bq', 'p': 43, 'prec': 20, 'unit': 4535696779654238609328088902231, 'val': 1}
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id: 174668
{'lmfdb_iso': '4800.bq', 'p': 47, 'prec': 20, 'unit': 36506293667057249217849767869174, 'val': 1}
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id: 174671
{'lmfdb_iso': '4800.bq', 'p': 53, 'prec': 20, 'unit': 482479855018520694648276042833853, 'val': 1}
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id: 174676
{'lmfdb_iso': '4800.bq', 'p': 59, 'prec': 20, 'unit': 2476054503532727573764483465224450, 'val': 1}
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id: 174677
{'lmfdb_iso': '4800.bq', 'p': 61, 'prec': 20, 'unit': 3382315610997247290207272740188988, 'val': 1}
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id: 174660
{'lmfdb_iso': '4800.bq', 'p': 67, 'prec': 20, 'unit': 7845544617360382078072058244758014, 'val': 1}
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id: 174675
{'lmfdb_iso': '4800.bq', 'p': 71, 'prec': 20, 'unit': 88407143209239923456324513492679690, 'val': 1}
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id: 174672
{'lmfdb_iso': '4800.bq', 'p': 73, 'prec': 20, 'unit': 98314179536782970290522333255691478, 'val': 1}
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id: 174674
{'lmfdb_iso': '4800.bq', 'p': 83, 'prec': 20, 'unit': 1814947982548954821636012916033474648, 'val': 1}
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id: 174659
{'lmfdb_iso': '4800.bq', 'p': 97, 'prec': 20, 'unit': 4764266435756224258765589809918256259, 'val': 1}