-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '732227823843101831', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 145.6471332868155, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [19, [1, 1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '18240.1', 'coefficient_field': '1.1.1.1', 'conductor': 18240, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1, -2, 17], [1, 1], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, 8, 43], [1, -8, 47], [1, -10, 53], [1, -12, 59], [1, -2, 61], [1, 4, 67], [1, -8, 71], [1, -2, 73], [1, 0, 79], [1, -4, 83], [1, 10, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 42, 'label': '2-18240-1.1-c1-0-42', 'leading_term': '4.67041519429', '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/18240/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.090262348194978, 1.700537693849111, 1.367494668584946, -0.06605566589094646, -2.10237115248847, -3.651060878455329, -3.694181712870973, -2.148377905794426, -0.1255855997653261, 0.8677003173202887, 0.2591103727856066, -1.007385401060124, -1.414949698526984, -0.5587569396477448, 0.2696824511709485, -0.4814100925208182, -2.558779800957596, -3.723674934858342, -2.129030649635467, 1.232638394414781, 3.137391640284702, 1.608514144098626, -1.645516428188701, -3.014798025764927, -1.167868479713065, 1.463903101713433, 1.883359895948116, 0.3529805581246431, -0.2216134996629534, 1.462104227812926, 3.140610980130284, 2.200109809374881, -0.4240506307410314, -1.403995236190522, 0.2440164893674219, 1.771713168944648, 0.851349735598983, -0.9302704881849061, -0.6899656883231845, 0.9767586675639994, 0.7795143007483704, -1.690326905299829, -2.452064970721932, 1.088907843468018, 5.526585213820146, 5.634280634827146, 1.69119607873419, -1.065686208768575, -0.1046043313806265, 1.373236748649169, 0.3421511362306629, -1.16309374882129, -0.0824619251583841, 1.901450860657018, 0.9826022662508567, -2.070524764946516, -2.80912492902681, -0.4649070816088547, 0.7401778708865432, -1.240206302863857, -2.914450305368798, -1.509968346890266, 0.2130929106188257, -0.8522871265584904, -2.42587828607572, -1.284874788839063, 0.04568516653901805, -2.669826474851149, -6.854830655758359, -5.903682381477985, -0.005468112035886967, 3.368329448799554, 0.8917997420662697, -2.150165055456796, -1.231762285778296, 0.8372610960847084, 0.4171044342300938, -0.6499938480548598, -0.008033823158518983, 0.0536511724080948, -2.127078733937813, -2.813843638584419, 0.5624663893727322, 3.414366817289071, 1.273867387872544, -2.052510675251816, -1.015386950684959, 1.901438076019274, 1.236615101527187, -1.145112233260861, -0.01283711020548383, 2.866579504300354, 2.204178704334639, -0.2375054029695625, 1.071527792967311, 4.26568572772051, 3.001351501099775, -1.552438437766978, -2.580795881508837, 0.1879721663153521, 1.033647211004161, -0.614730994486379, -0.4441154266033151, 1.041113566844392, -0.113507744838382, -2.265605579914056, -1.161442126000483, 0.8114937988793903, -0.8621812208560387, -2.844266124722257, 0.2022596390092777, 4.357350534948445, 2.966716622361876, -0.7416884240663074, 0.1354202074851411, 3.129485484048307, 2.090670832535434, -0.4747180272974995, 0.658896691591978, 2.158797778106839], 'positive_zeros': ['0.9911601774516588', '2.268689270581132', '2.801411818131566', '3.631338029744285', '3.912126853355947', '4.909462244334021', '5.622576779192431', '6.350108702318736', '7.064194477012753', '7.307809838265882', '8.206881154234096', '8.722301150775336', '9.355976751480663', '9.852110294904621', '10.34030771647577', '10.94343291036844', '11.86288665701360', '12.26288462490071', '12.79312557989403', '13.25913387426166', '13.83266506829141', '14.54813875318574', '14.87723546833326', '15.68744512267124', '15.87766283303192', '16.68816269122319', '16.76995079031385', '17.75022974088450', '18.30593906537639', '18.87585155990132', '19.32246987580065', '19.75203427654019'], 'prelabel': '2-18240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.068435411718268, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 732227823843101831, 'z1': {'__RealLiteral__': 0, 'data': '0.9911601774516588', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.268689270581132', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.801411818131566', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 145.6471332868155, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 18240, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, -4, 0, 1, 0, 0, 0, -2, 0, -1, 0, 2, 0, -1, 0, -4, 0, 0, 0, 1, 0, 1, 0, 6, 0, -8, 0, 0, 0, 4, 0, -2, 0, -2, 0, 6, 0, -8, 0, -1, 0, 8, 0, 9, 0, 2, 0, 10, 0, 0, 0, -1, 0, 12, 0, 2, 0, -4, 0, 2, 0, -4, 0, 0, 0, 8, 0, 2, 0, 1, 0, 0, 0, 0, 0, 1, 0, 4, 0, -2, 0, 6, 0, -10, 0, 8, 0, -8, 0, 1, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 2, 37], 'euler41': [1, -6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, -10, 53], 'euler59': [1, -12, 59], 'euler61': [1, -2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -2, 73], 'euler79': [1, 0, 79], 'euler83': [1, -4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 4, 7], [1, 0, 11], [1, 2, 13], [1, -2, 17], [1, 1, 0], [1, 0, 23], [1, -6, 29], [1, 8, 31], [1, 2, 37], [1, -6, 41], [1, 8, 43], [1, -8, 47], [1, -10, 53], [1, -12, 59], [1, -2, 61], [1, 4, 67], [1, -8, 71], [1, -2, 73], [1, 0, 79], [1, -4, 83], [1, 10, 89], [1, -6, 97]], 'index': 42, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/18240/bp'], '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': '2-18240-1.1-c1-0-42', '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': '2-18240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.068435411718268, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 732227823843101831, 'z1': {'__RealLiteral__': 0, 'data': '0.9911601774516588', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '732227823843101831', 'Lhash_array': ['732227823843101831'], 'label': '2-18240-1.1-c1-0-42', 'type': 'ECQ', 'url': 'EllipticCurve/Q/18240/bp'}