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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 0, 'Lhash': '1790416647117733810', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 139.13134048187902, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '17424.1', 'coefficient_field': '1.1.1.1', 'conductor': 17424, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, -4, 7], [1], [1, 6, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, 2, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 59, 'label': '2-132e2-1.1-c1-0-59', 'leading_term': '6.39666146128', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'EllipticCurve/Q/17424/bx', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.536038609800027, 2.668197543489459, 2.964853788717316, 2.219468199004121, 0.7841936504205997, -0.4657986486109884, -0.7220398025185101, -0.005921877954836226, 0.6473312560627932, 0.01130865688824452, -2.038579783319378, -4.03381416609978, -4.023109595157735, -1.507077138263542, 1.74622857535266, 3.154860041971356, 1.833768178533662, -0.5006853906351029, -1.427694782514832, -0.5320692182014445, 0.2724269827160492, -0.6573039395286608, -2.345492650707195, -2.280644581526095, 0.1669979490088505, 2.449378160142305, 1.771804161776208, -1.255303913712213, -3.182454053060828, -2.100472214973127, -0.07029345509060463, -0.1432739725914712, -1.970921157868851, -2.274010936119876, 0.2881601039621802, 2.849944842222307, 2.227290767972429, -0.5228669732539789, -1.669886498081815, -0.3153945399837718, 0.4655792827452356, -1.31753172468056, -3.163586323137137, -1.896080973711122, 1.097723499493613, 1.697761389072125, -0.5494638966551296, -1.619327421276057, 0.5802081011953697, 2.707804163352254, 1.285762477714498, -1.53877403662758, -1.241308103134617, 1.866260304793393, 3.156649368430121, 1.044044468072262, -0.9575781700315286, -0.505484012770249, 0.1169639800251042, -0.7033074947303231, 0.1975979252081025, 5.288727975343258, 10.25752198534303, 8.958570843036247, 2.648053821034972, -1.583741667806287, -0.9734176842420885, 0.4557806845720227, -0.02138398772076649, 0.02778991752684526, 1.926548786987678, 2.321793552097441, -0.4718991808911134, -2.406573782544024, -0.6328269147145246, 0.8156366884585865, -2.075737992836393, -5.489805943416397, -3.689938172605511, 1.060775297812072, 2.160556725051962, -0.4654872393940786, -1.326253416654092, 0.5636952660842816, 1.101677580402089, -0.3036130916674242, -0.3397633676017466, 0.1920169001244946, -2.880390996042308, -7.765513590454342, -7.595230514986644, -2.07869620963474, 1.265025414556031, -0.4924553740271782, -1.819304268979018, 0.2210353817929022, 1.176951324833931, -1.150675208834274, -2.312163837424543, -0.3419111891917896, 0.5278678333413342, -0.8568393549485883, 0.3437067885868816, 4.675705488894946, 5.649441241167311, 1.422280656574094, -1.414273845736388, 0.2253822153954264, 1.179585362868962, -0.9304152318826878, -1.496311802893666, 0.4547390044984965, -0.5550207691846717, -4.89963864463264, -5.671889689721344, -1.452238743191547, 1.001705782217357, -0.5699811885474336, -1.06372360364989, 0.6224231098034326], 'positive_zeros': ['1.389624160696307', '2.001616135373072', '2.501922905820217', '3.610240274551057', '4.440614245486270', '5.116715206704746', '5.382931676298422', '6.235915256397293', '6.902734681609384', '7.764293523412562', '7.971488754196930', '8.727933511872652', '9.450922567286075', '10.04893382159807', '10.35170860319082', '11.15210402493362', '11.69576637667248', '12.20142058046745', '12.85272040668667', '13.35769298296746', '14.09908903681726', '14.62791225472520', '14.81097742985787', '15.23314572569715', '16.36919347050276', '16.88395508691172', '17.24350574139074', '17.49416588463944', '18.21469913886378', '18.81142220051840', '19.11338672873394', '19.93733113922303'], 'prelabel': '2-132e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.79539488452502, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1790416647117733810, 'z1': {'__RealLiteral__': 0, 'data': '1.389624160696307', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.001616135373072', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.501922905820217', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 139.13134048187902, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 17424, 'conductor_radical': 66, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 4, 0, 0, 0, 0, 0, -6, 0, 0, 0, 6, 0, -8, 0, 0, 0, 0, 0, -1, 0, 0, 0, -6, 0, 0, 0, 0, 0, 8, 0, 6, 0, 0, 0, -10, 0, -8, 0, 0, 0, 0, 0, 9, 0, 0, 0, -6, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, -12, 0, 12, 0, 0, 0, -8, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 12, 0, 12, 0, 0, 0, 6, 0, -24, 0, 0, 0, -16, 0, 2, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 10, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, 4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, -4, 7], [1, 0, 0], [1, 6, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 6, 29], [1, 0, 31], [1, -6, 37], [1, 10, 41], [1, 8, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -2, 61], [1, -12, 67], [1, 8, 71], [1, 2, 73], [1, 4, 79], [1, -12, 83], [1, -6, 89], [1, -2, 97]], 'index': 59, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/17424/bx'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-132e2-1.1-c1-0-59', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-132e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.79539488452502, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1790416647117733810, 'z1': {'__RealLiteral__': 0, 'data': '1.389624160696307', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1790416647117733810', 'Lhash_array': ['1790416647117733810'], 'label': '2-132e2-1.1-c1-0-59', 'type': 'ECQ', 'url': 'EllipticCurve/Q/17424/bx'}