-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 2, 'A8': 0, 'A9': 0, 'Lhash': '910458484614752768', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 2260.8842828305337, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [11, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '283140.1', 'coefficient_field': '1.1.1.1', 'conductor': 283140, 'conductor_radical': 4290, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -2, 7], [1], [1, 1], [1, 2, 17], [1, -8, 19], [1, 8, 23], [1, 0, 29], [1, 4, 31], [1, -2, 37], [1, -4, 41], [1, 2, 43], [1, 0, 47], [1, 6, 53], [1, 4, 59], [1, -4, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 14, 83], [1, -10, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-283140-1.1-c1-0-26', 'leading_term': '7.4936650328', '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/283140/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.593848868086549, 1.721642652120829, 0.03878029460694911, -1.96088060848513, -2.116105009521592, -0.2741889428660692, 0.9904363190025297, -0.4127067586797523, -2.768579103278226, -2.508945799935443, 0.4178724865634695, 1.93100513763521, -0.1015939745625789, -2.301526415691812, -1.131750471947856, 1.2041583438352, 0.631384986368701, -1.502119611164453, -0.9193750275857726, 1.448956643663356, 1.06872352080774, -1.210039793459803, -0.2517265787321159, 3.134291737340493, 2.708589569607586, -1.457192672643867, -2.380141930186821, 1.14237977364524, 2.680500473452847, 0.5400445680473285, -0.3024044865566074, 0.4850089084505385, -1.419442383689744, -3.980541809840666, -1.860072715739085, 1.658360429337798, 0.3950151536438203, -1.931397904439055, 0.430339674166842, 2.709771612071436, -0.2024902322863905, -2.347537602448941, 0.8385266418784086, 2.994279057164724, 0.6313116170408453, -0.5881966281321972, 0.289195909310129, -1.500405994890323, -3.201543593495282, -0.246641199237151, 1.33695924126516, -2.856695018936011, -4.679430663042448, -0.343036219513549, 1.627686215673283, -0.8314079120496524, -0.5566003257469414, 1.160331437968623, -0.9721283924749708, -1.826984805524676, 2.194448026036755, 3.541428527727772, 0.4698602634247328, 0.04249416019242095, 0.4345930402247748, -3.226397069604529, -4.078069776798094, 1.329918663603578, 3.256766869883584, -0.2405136368047255, -0.4501203299136026, 1.31818227357508, -0.2237779875079293, 0.2474457304970213, 3.58378701764195, 1.235014191564877, -3.702077879381473, -1.850412158525632, 1.591867342682017, 0.3517402945957412, 0.2144489538764917, 1.305579505680138, -1.733137130463831, -2.59369813405896, 2.588833198674265, 3.713206547412576, -0.3700599598887254, -0.3607346392735064, 0.5942615824485787, -2.448212444978515, -1.87571715454001, 1.913202995456054, -0.5018913598740802, -4.152733877215302, -1.554502819500029, 0.3972556332985487, -0.52679380502624, 0.8863079984118885, 0.0131084940241764, -4.117930564798769, -1.788098431040622, 2.799298491211503, -0.8181847943668826, -4.189080565035926, -0.5070142963303371, 0.6539189917880657, -1.310235387812159, 0.1402012887859651, -0.2956456635745205, -3.366403532357561, -1.32269593581651, 1.02658078597246, -0.9355704178236635, 0.7792477054736602, 3.611029806680967, -0.1162625238486864, -1.288778757108839, 3.375663650014432, 2.340856026638951, -1.291263520063993], 'positive_zeros': ['0.7543474445674610', '1.533481880620136', '1.956500066186182', '2.716093667613140', '3.241485581240695', '3.854816090814228', '4.318390932371862', '4.841611122734662', '5.357972798048876', '5.769608729423242', '6.412571263808626', '6.926603553426551', '7.568429964383784', '7.831444885303089', '8.120724363276401', '8.859114854190901', '9.280102437878517', '9.721768232635935', '10.23773405326371', '10.70026676374289', '11.31155380851590', '11.64029701563295', '11.84672220311053', '12.51596667639370', '12.85546172538257', '13.51855438471962', '13.91793723096607', '14.30817836879364', '14.67044098436185', '15.12981901526193', '15.80393652727924', '15.99180077730030', '16.29758829023440', '16.94333559736280', '17.48085890262956', '17.79832470288205', '18.22187806980245', '18.47880472190604', '19.05259929129013', '19.60136110908992'], 'prelabel': '2-283140-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.548756901001454, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 910458484614752768, 'z1': {'__RealLiteral__': 0, 'data': '0.7543474445674610', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.533481880620136', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.956500066186182', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2260.8842828305337, 'bad_primes': [2, 3, 5, 11, 13], 'central_character': '1.1', 'conductor': 283140, 'conductor_radical': 4290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 2, 0, 0, 0, 0, 0, -1, 0, 0, 0, -2, 0, 8, 0, 0, 0, -8, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, -2, 0, 2, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -3, 0, 0, 0, -6, 0, 0, 0, 0, 0, -4, 0, 4, 0, 0, 0, 1, 0, 4, 0, 0, 0, -8, 0, -2, 0, 0, 0, 0, 0, 8, 0, 0, 0, -14, 0, 2, 0, 0, 0, 10, 0, -2, 0, 0, 0, -8, 0, 18, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -4, 41], 'euler43': [1, 2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 4, 59], 'euler61': [1, -4, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, 8, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 14, 83], 'euler89': [1, -10, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -2, 7], [1, 0, 0], [1, 1, 0], [1, 2, 17], [1, -8, 19], [1, 8, 23], [1, 0, 29], [1, 4, 31], [1, -2, 37], [1, -4, 41], [1, 2, 43], [1, 0, 47], [1, 6, 53], [1, 4, 59], [1, -4, 61], [1, -4, 67], [1, 8, 71], [1, 2, 73], [1, -8, 79], [1, 14, 83], [1, -10, 89], [1, -18, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/283140/l'], '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': '2-283140-1.1-c1-0-26', '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': '2-283140-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 47.548756901001454, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 910458484614752768, 'z1': {'__RealLiteral__': 0, 'data': '0.7543474445674610', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '910458484614752768', 'Lhash_array': ['910458484614752768'], 'factors': ['2-283140-1.1-c1-0-26'], 'label': '2-283140-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/283140/l'}