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ec_curvedata • Show schema
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{'Ciso': '800i', 'Clabel': '800i1', 'Cnumber': 1, 'abc_quality': 0.9949912704917342, 'absD': 200000000, 'adelic_genus': 3, 'adelic_index': 60, 'adelic_level': 40, 'ainvs': [0, -1, 0, -208, 1412], 'analytic_rank': 1, 'bad_primes': [2, 5], 'class_deg': 1, 'class_size': 1, 'cm': 0, 'conductor': 800, 'degree': 240, 'elladic_images': ['8.2.0.1', '5.15.0.1'], 'faltings_height': {'__RealLiteral__': 0, 'data': '0.31558410008219759058368225303', 'prec': 103}, 'faltings_index': 0, 'faltings_ratio': 1, 'iso_nlabel': 1, 'isogeny_degrees': [1], 'jinv': [-5000, 1], 'lmfdb_iso': '800.b', 'lmfdb_label': '800.b1', 'lmfdb_number': 1, 'manin_constant': 1, 'min_quad_twist_ainvs': [0, -1, 0, -8, -8], 'min_quad_twist_disc': -20, 'modell_images': ['5Ns'], 'modm_images': ['5.15.0.a.1', '8.2.0.a.1', '20.30.0.b.1', '40.60.3.u.1'], 'nonmax_primes': [2, 5], 'nonmax_rad': 10, 'num_bad_primes': 2, 'num_int_pts': 6, 'optimality': 1, 'potential_good_reduction': True, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.19637779133168667685371410477', 'prec': 103}, 'semistable': False, 'serre_invariants': [[2, 4, 25], [5, 10, 32]], 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '-1.2772348936271616412130813935', 'prec': 103}, 'szpiro_ratio': 4.177933179061148, '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, 2, 0, -2, 0, -5, 0, 0, 0, 0, 0, 5, 0, -5, 0], 'aplist': [0, -1, 0, 2, -5, 0, 5, -5, -6, 4, -10, -10, 5, -4, 8, -10, 0, -10, -3, 0, -5, -10, 1, -9, 10], 'class_deg': 1, 'class_size': 1, 'conductor': 800, 'isogeny_matrix': [[1]], 'lmfdb_iso': '800.b', 'trace_hash': 584720505788691135}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.53196999044771910407456934002', 'prec': 103}, 'conductor': 800, 'gens': [[-8, 50, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.19637779133168667685371410477', 'prec': 103}], 'lmfdb_label': '800.b1', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '1.7115587321269884745620801932', 'prec': 100}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.0166727412973597372967082909344774460', 'prec': 130}, 'tamagawa_product': 6, 'torsion_generators': [], 'xcoord_integral_points': [-8, 8, 17]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': 'a', '3': [1, 0], '5': 'a', '7': [1, 0], '11': [3, 0], '13': [1, 1, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [1, 0], '43': [1, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '800.b1'}
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ec_torsion_growth • Show schema
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id: 37819
{'degree': 3, 'field': [2, 2, -1, 1], 'lmfdb_label': '800.b1', 'torsion': [2]}
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id: 37820
{'degree': 6, 'field': [2, 0, -3, 0, 4, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [2, 2]}
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id: 37821
{'degree': 8, 'field': [-3, 0, 16, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [3]}
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id: 37822
{'degree': 8, 'field': [45, 0, 40, 0, 10, 0, 0, 0, 1], 'lmfdb_label': '800.b1', 'torsion': [5]}
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id: 37823
{'degree': 12, 'field': [1, -1, 0, -1, -3, -4, 0, -4, -3, -1, 0, -1, 1], 'lmfdb_label': '800.b1', 'torsion': [4]}
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id: 37824
{'degree': 16, 'field': [-4, 8, 0, 40, -240, 704, -1488, 2240, -2350, 1740, -888, 256, 20, -60, 30, -8, 1], 'lmfdb_label': '800.b1', 'torsion': [5]}
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ec_localdata • Show schema
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id: 10362
{'conductor': 800, 'conductor_valuation': 5, 'discriminant_valuation': 9, 'j_denominator_valuation': 0, 'kodaira_symbol': -1, 'lmfdb_label': '800.b1', 'prime': 2, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 10363
{'conductor': 800, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 0, 'kodaira_symbol': -4, 'lmfdb_label': '800.b1', 'prime': 5, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 3}
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ec_galrep • Show schema
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id: 1669685
{'adelic_gens': [[21, 0, 0, 21], [31, 32, 8, 39], [1, 16, 0, 9], [31, 10, 20, 31], [31, 30, 30, 11], [21, 20, 20, 21], [31, 0, 0, 31], [9, 0, 0, 9], [1, 20, 0, 1], [31, 25, 25, 6], [9, 8, 15, 23], [33, 0, 0, 33], [31, 22, 3, 9]], 'adelic_image': '40.60.3.?', 'conductor': 800, 'lmfdb_label': '800.b1', 'prime': 0}
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id: 3695
{'conductor': 800, 'elladic_image': '8.2.0.1', 'lmfdb_label': '800.b1', 'modell_image': '2G', 'prime': 2}
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id: 3696
{'conductor': 800, 'elladic_image': '5.15.0.1', 'lmfdb_label': '800.b1', 'modell_image': '5Ns', 'prime': 5}
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ec_padic • Show schema
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id: 16059
{'lmfdb_iso': '800.b', 'p': 7, 'prec': 20, 'unit': 1107788330306513, 'val': 1}
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id: 16064
{'lmfdb_iso': '800.b', 'p': 11, 'prec': 20, 'unit': 792215766665271089, 'val': 2}
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id: 16065
{'lmfdb_iso': '800.b', 'p': 17, 'prec': 20, 'unit': 100219055035163990300291, 'val': 1}
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id: 16066
{'lmfdb_iso': '800.b', 'p': 19, 'prec': 20, 'unit': 1525480882377546442100803, 'val': 1}
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id: 16069
{'lmfdb_iso': '800.b', 'p': 23, 'prec': 20, 'unit': 21470884513692961231318297, 'val': 1}
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id: 16062
{'lmfdb_iso': '800.b', 'p': 29, 'prec': 20, 'unit': 4900626369337410160950111623, 'val': 1}
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id: 16073
{'lmfdb_iso': '800.b', 'p': 31, 'prec': 20, 'unit': 6962776620787686526174507570, 'val': 1}
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id: 16058
{'lmfdb_iso': '800.b', 'p': 37, 'prec': 20, 'unit': 618416071064487712529699510583, 'val': 1}
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id: 16060
{'lmfdb_iso': '800.b', 'p': 41, 'prec': 20, 'unit': 3166441722693993744720642276273, 'val': 1}
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id: 16061
{'lmfdb_iso': '800.b', 'p': 43, 'prec': 20, 'unit': 10666408217849414027280846661214, 'val': 1}
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id: 16063
{'lmfdb_iso': '800.b', 'p': 47, 'prec': 20, 'unit': 15430150324071953206336636107898, 'val': 1}
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id: 16067
{'lmfdb_iso': '800.b', 'p': 53, 'prec': 20, 'unit': 438176343122214022938741045535982, 'val': 1}
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id: 16072
{'lmfdb_iso': '800.b', 'p': 61, 'prec': 20, 'unit': 1182092151189312962216895429547076, 'val': 1}
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id: 16057
{'lmfdb_iso': '800.b', 'p': 67, 'prec': 20, 'unit': 25950069572273359165836528277105825, 'val': 1}
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id: 16068
{'lmfdb_iso': '800.b', 'p': 73, 'prec': 20, 'unit': 88385223046069637372757556319521947, 'val': 1}
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id: 16071
{'lmfdb_iso': '800.b', 'p': 79, 'prec': 20, 'unit': 1023997553933470094741840047870225986, 'val': 1}
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id: 16056
{'lmfdb_iso': '800.b', 'p': 83, 'prec': 20, 'unit': 232854974048109806498705281203942656515, 'val': -1}
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id: 16070
{'lmfdb_iso': '800.b', 'p': 89, 'prec': 20, 'unit': 585742078672356756773405127358831931, 'val': 1}
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id: 16055
{'lmfdb_iso': '800.b', 'p': 97, 'prec': 20, 'unit': 26582289416445576227339793616030629373, 'val': 1}