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ec_curvedata • Show schema
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{'Ciso': '585f', 'Clabel': '585f6', 'Cnumber': 6, 'abc_quality': 1.0149811194984983, 'absD': 133800231512025, 'adelic_genus': 13, 'adelic_index': 768, 'adelic_level': 6240, 'ainvs': [1, -1, 0, 5445, 533250], 'analytic_rank': 1, 'bad_primes': [3, 5, 13], 'class_deg': 16, 'class_size': 8, 'cm': 0, 'conductor': 585, 'degree': 1536, 'elladic_images': ['8.48.0.196'], 'faltings_height': {'__RealLiteral__': 0, 'data': '1.3921496218487160779632034313', 'prec': 100}, 'faltings_index': 5, 'faltings_ratio': 8, 'iso_nlabel': 6, 'isogeny_degrees': [1, 2, 4, 8], 'jinv': [24487529386319, 183539412225], 'lmfdb_iso': '585.g', 'lmfdb_label': '585.g8', 'lmfdb_number': 8, 'manin_constant': 1, 'min_quad_twist_ainvs': [1, 0, 0, 605, -19750], 'min_quad_twist_disc': -3, 'modell_images': ['2B'], 'modm_images': ['2.3.0.a.1', '4.12.0.d.1', '8.48.0-8.q.1.4', '12.24.0-4.d.1.1', '24.96.0-24.be.2.11', '40.96.0-40.bf.1.12', '120.192.1.?', '208.96.0.?', '416.192.2.?', '624.192.1.?', '1040.192.1.?', '1248.384.5.?', '2080.384.5.?', '3120.384.5.?', '6240.768.13.?'], 'nonmax_primes': [2], 'nonmax_rad': 2, 'num_bad_primes': 3, 'num_int_pts': 4, 'optimality': 0, 'potential_good_reduction': False, 'rank': 1, 'regulator': {'__RealLiteral__': 0, 'data': '0.69310690167684312650666402659', 'prec': 103}, 'semistable': False, 'sha': 1, 'sha_primes': [], 'signD': -1, 'stable_faltings_height': {'__RealLiteral__': 0, 'data': '0.84284347751466123226558081284', 'prec': 103}, 'szpiro_ratio': 6.262424113375516, '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, -1, 0, 0, -3, 0, -1, -4, 0, 1, 0, 0, -1, -2, 0, -4, 1], 'aplist': [1, 0, -1, 0, -4, 1, -2, -4, -8, 2, -8, 6, 6, -4, 8, -6, 12, -2, -4, 0, -6, 16, 4, -10, 18], 'class_deg': 16, 'class_size': 8, 'conductor': 585, 'isogeny_matrix': [[1, 2, 4, 4, 8, 16, 16, 8], [2, 1, 2, 2, 4, 8, 8, 4], [4, 2, 1, 4, 8, 16, 16, 8], [4, 2, 4, 1, 2, 4, 4, 2], [8, 4, 8, 2, 1, 2, 2, 4], [16, 8, 16, 4, 2, 1, 4, 8], [16, 8, 16, 4, 2, 4, 1, 8], [8, 4, 8, 2, 4, 8, 8, 1]], 'lmfdb_iso': '585.g', 'trace_hash': 2111954834260030367}
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ec_mwbsd • Show schema
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{'area': {'__RealLiteral__': 0, 'data': '0.061772361239014509606913686065', 'prec': 107}, 'conductor': 585, 'gens': [[-30, 600, 1]], 'heights': [{'__RealLiteral__': 0, 'data': '0.69310690167684312650666402659', 'prec': 103}], 'lmfdb_label': '585.g8', 'ngens': 1, 'rank_bounds': [1, 1], 'real_period': {'__RealLiteral__': 0, 'data': '0.42554072646310054843282797780', 'prec': 103}, 'sha_an': {'__RealLiteral__': 0, 'data': '1.0000000000000000000000000000', 'prec': 100}, 'special_value': {'__RealLiteral__': 0, 'data': '2.3595617156492210218470390653000644197', 'prec': 130}, 'tamagawa_product': 32, 'torsion_generators': [[-237, 237, 2]], 'xcoord_integral_points': [-30, 490]}
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ec_iwasawa • Show schema
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{'iwdata': {'2': [2, 1], '3': 'a', '5': [1, 0], '7': [1, 1, 0], '11': [1, 0], '13': [2, 0], '17': [1, 0], '19': [1, 0], '23': [1, 0], '29': [1, 0], '31': [1, 0], '37': [1, 0], '41': [3, 0], '43': [3, 0], '47': [1, 0]}, 'iwp0': 0, 'lmfdb_label': '585.g8'}
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ec_torsion_growth • Show schema
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id: 26887
{'degree': 2, 'field': [-3, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [4]}
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id: 26888
{'degree': 2, 'field': [1, -1, 1], 'lmfdb_label': '585.g8', 'torsion': [8]}
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id: 26886
{'degree': 2, 'field': [1, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [2, 2]}
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id: 26889
{'degree': 4, 'field': [1, 0, -1, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [2, 8]}
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id: 26890
{'degree': 4, 'field': [25, 0, -20, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [8]}
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id: 26891
{'degree': 4, 'field': [25, 0, 20, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [8]}
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id: 26893
{'degree': 8, 'field': [1, -3, 11, -21, 36, -21, 11, -3, 1], 'lmfdb_label': '585.g8', 'torsion': [16]}
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id: 26894
{'degree': 8, 'field': [3, -219, 264, -81, 27, 0, 4, -4, 1], 'lmfdb_label': '585.g8', 'torsion': [6]}
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id: 26892
{'degree': 8, 'field': [625, 0, 0, 0, -25, 0, 0, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [4, 8]}
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id: 26895
{'degree': 16, 'field': [1, 0, -13, 0, 67, 0, -247, 0, 640, 0, -247, 0, 67, 0, -13, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [2, 16]}
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id: 26901
{'degree': 16, 'field': [9, 0, -219, 0, 5311, 0, -438, 0, 39, 0, -146, 0, 6, 0, 0, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [24]}
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id: 26899
{'degree': 16, 'field': [25, 0, 33554, 0, 26611, 0, -7213, 0, 535, 0, -310, 0, 82, 0, 8, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [2, 6]}
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id: 26900
{'degree': 16, 'field': [18225, 0, 19197, 0, 3240, 0, -2511, 0, 297, 0, -225, 0, -45, 0, -6, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [12]}
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id: 26898
{'degree': 16, 'field': [9150625, 0, 0, 0, 13245000, 0, 0, 0, 816050, 0, 0, 0, 1800, 0, 0, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [16]}
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id: 26896
{'degree': 16, 'field': [31640625, 0, 0, 0, 4640625, 0, 0, 0, 675000, 0, 0, 0, 825, 0, 0, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [2, 16]}
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id: 26897
{'degree': 16, 'field': [1171350625, 0, 0, 0, -52977000, 0, 0, 0, 504050, 0, 0, 0, -1320, 0, 0, 0, 1], 'lmfdb_label': '585.g8', 'torsion': [16]}
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ec_localdata • Show schema
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id: 6896
{'conductor': 585, 'conductor_valuation': 2, 'discriminant_valuation': 8, 'j_denominator_valuation': 2, 'kodaira_symbol': -6, 'lmfdb_label': '585.g8', 'prime': 3, 'reduction_type': 0, 'root_number': -1, 'tamagawa_number': 2}
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id: 6897
{'conductor': 585, 'conductor_valuation': 1, 'discriminant_valuation': 2, 'j_denominator_valuation': 2, 'kodaira_symbol': 6, 'lmfdb_label': '585.g8', 'prime': 5, 'reduction_type': -1, 'root_number': 1, 'tamagawa_number': 2}
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id: 6898
{'conductor': 585, 'conductor_valuation': 1, 'discriminant_valuation': 8, 'j_denominator_valuation': 8, 'kodaira_symbol': 12, 'lmfdb_label': '585.g8', 'prime': 13, 'reduction_type': 1, 'root_number': -1, 'tamagawa_number': 8}
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ec_galrep • Show schema
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id: 1668500
{'adelic_gens': [[1, 0, 32, 1], [1, 32, 0, 1], [2051, 6232, 1026, 283], [25, 16, 4504, 5129], [6209, 32, 6208, 33], [25, 16, 2358, 5353], [5761, 24, 0, 1], [13, 16, 1694, 1305], [1, 32, 4, 129], [3135, 32, 5257, 4065]], 'adelic_image': '6240.768.13.?', 'conductor': 585, 'lmfdb_label': '585.g8', 'prime': 0}
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id: 2651
{'conductor': 585, 'elladic_image': '8.48.0.196', 'lmfdb_label': '585.g8', 'modell_image': '2B', 'prime': 2}
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ec_padic • Show schema
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id: 9699
{'lmfdb_iso': '585.g', 'p': 11, 'prec': 20, 'unit': 16013100267972068784, 'val': 1}
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id: 9700
{'lmfdb_iso': '585.g', 'p': 17, 'prec': 20, 'unit': 35120177210824288338119, 'val': 1}
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id: 9701
{'lmfdb_iso': '585.g', 'p': 19, 'prec': 20, 'unit': 651052145223180998370903, 'val': 1}
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id: 9705
{'lmfdb_iso': '585.g', 'p': 23, 'prec': 20, 'unit': 58345023726429919312042012, 'val': 1}
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id: 9697
{'lmfdb_iso': '585.g', 'p': 29, 'prec': 20, 'unit': 910558596440296042638800282, 'val': 1}
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id: 9709
{'lmfdb_iso': '585.g', 'p': 31, 'prec': 20, 'unit': 13817312446284561775532590957, 'val': 1}
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id: 9694
{'lmfdb_iso': '585.g', 'p': 37, 'prec': 20, 'unit': 372065588683631777328460308160, 'val': 1}
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id: 9695
{'lmfdb_iso': '585.g', 'p': 41, 'prec': 20, 'unit': 43784025659963139909210835955, 'val': 2}
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id: 9696
{'lmfdb_iso': '585.g', 'p': 43, 'prec': 20, 'unit': 227052847789474296807602942361, 'val': 2}
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id: 9707
{'lmfdb_iso': '585.g', 'p': 47, 'prec': 20, 'unit': 26033595884365580367573620402312, 'val': 1}
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id: 9702
{'lmfdb_iso': '585.g', 'p': 53, 'prec': 20, 'unit': 276452619783216140586934914074453, 'val': 1}
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id: 9703
{'lmfdb_iso': '585.g', 'p': 59, 'prec': 20, 'unit': 4024267493321312974300292229703454, 'val': 1}
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id: 9708
{'lmfdb_iso': '585.g', 'p': 61, 'prec': 20, 'unit': 1331573992257849700893633124218031, 'val': 1}
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id: 9693
{'lmfdb_iso': '585.g', 'p': 67, 'prec': 20, 'unit': 21498949128845455076595362464099008, 'val': 1}
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id: 9704
{'lmfdb_iso': '585.g', 'p': 73, 'prec': 20, 'unit': 185522389025820476607965556909581512, 'val': 1}
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id: 9698
{'lmfdb_iso': '585.g', 'p': 79, 'prec': 20, 'unit': 1108961753690929885861261163159428217, 'val': 1}
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id: 9692
{'lmfdb_iso': '585.g', 'p': 83, 'prec': 20, 'unit': 1478906946209906497274382548179692729, 'val': 1}
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id: 9706
{'lmfdb_iso': '585.g', 'p': 89, 'prec': 20, 'unit': 1071959568932041080113490200328008244, 'val': 1}
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id: 9691
{'lmfdb_iso': '585.g', 'p': 97, 'prec': 20, 'unit': 45858660479805897530536489361898090612, 'val': 1}