Formats: - HTML - YAML - JSON - 2026-09-20T17:22:29.818239
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': -1, 'A3': 1, 'A4': -1, 'A5': 0, 'A6': -1, 'A7': -4, 'A8': 3, 'A9': 1, 'Lhash': '454787070293974188', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [-1.5118578920369088, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1922.9973066774858, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1, -1]], [5, [1]], [13, [1]], [19, [1, 1]]], 'bad_primes': [3, 5, 13, 19], 'central_character': '240825.1', 'coefficient_field': '1.1.1.1', 'conductor': 240825, 'conductor_radical': 3705, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1], [1, 4, 7], [1, 0, 11], [1], [1, 2, 17], [1, 1], [1, -8, 23], [1, -2, 29], [1, 8, 31], [1, -2, 37], [1, -2, 41], [1, 0, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -14, 61], [1, 12, 67], [1, -8, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, 14, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-240825-1.1-c1-0-12', 'leading_term': '1.23569236238', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/240825/s', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 7}, 'plot_values': [1.235692362376533, 0.7088505855011119, -0.345973944336283, -0.6654645838401394, 0.5697519176849182, 2.373293399218573, 2.493300484533571, 0.1851155658503786, -2.149422240820502, -1.576893274576704, 1.20383903190837, 2.383283332303915, 0.4890371334991111, -1.247627702278234, -0.06437328178650967, 1.480846647852387, -0.2763470143652902, -3.103574089789556, -1.852515945872808, 2.172182959795389, 2.113900193183721, -2.769593926735429, -4.588452972437033, 0.3641074390601357, 4.842641271860876, 2.490588705994425, -1.95391614201888, -1.78862918791048, 0.4149887756504775, -0.5042843529968938, -2.048366534243611, 0.002711173732759086, 2.582559061324033, 1.483889613095339, -0.6162911395494202, -0.2941303580069619, 0.2804904117139127, -0.5756644980642761, -0.5674886544889802, 0.075652081749248, -1.20241946167778, -1.960961320375098, 0.7472220138843638, 2.184003679570362, -0.580891332125683, 0.421358192911076, 8.729209792939185, 12.39933128047336, 4.25743719090019, -4.023766447850813, -2.971347650098957, 0.2032312590169397, -0.2922662558289617, 0.2812461450054186, 1.709385967288084, -1.240819382950151, -3.989614516764247, -0.7792384804005862, 1.182611598652429, -2.973672129016516, -4.236986170558637, 0.4613449288995926, 1.336243150670329, -2.480442943039143, -2.012007403628482, 1.083791724284153, 0.1518308861099447, -0.5876938920572409, 2.152090993177155, 1.892099812498429, -1.39844213826919, -0.3374820321088783, 2.609595573938508, 1.208296724263513, -0.5281576158289022, 0.7627316785174912, 0.7312597142946108, -0.5116151891335401, -0.01021639025709573, -0.6899976443154014, -1.794948906944878, 1.483555960416161, 3.323883242684847, -1.564488806038727, -2.569204471003031, 4.268439029910056, 5.273557589631125, -1.024407476927749, -1.693957084609937, 1.000296871047327, -1.148040479082994, -1.242204129221115, 2.504173749663851, 0.2950345754116652, -3.021946563300002, 1.393506592093176, 1.823358009318071, -7.659936009819658, -10.46965054404206, -2.581298552930906, 1.213574356074525, -0.486196117551609, -0.05449291608158599, -0.1010356935906569, -1.490759649205545, -0.1139581731468217, 0.7516709883101732, -0.6198970209846719, -0.006848729663180557, -0.1104368495508894, -2.611794609700881, -0.6843844995948037, 3.148764053820502, 1.119905785414832, -0.7871960184535363, 1.399969563124383, 0.5882647002421688, -0.5003226092828071, 2.288774418330914, -0.7277498909461063, -7.405898108557318], 'positive_zeros': ['0.4149877036933776', '0.9162619668593431', '1.765825351911905', '2.395349047741549', '3.048408601269119', '3.507370382163851', '3.978104832563054', '4.611575814523644', '5.119102669637005', '5.735899040984754', '6.372757107680719', '6.930637276438148', '7.189501207604750', '7.749798087513000', '8.400909966401974', '8.819297888995773', '9.105223183450264', '9.667236740023965', '9.796938036024791', '10.44506730091531', '10.95142623392004', '11.22962928745314', '12.10140644678534', '12.71539765411960', '12.93052155006755', '13.21228463550733', '13.67853180439240', '14.29541205270297', '14.59671931380212', '15.22521423027317', '15.59096707506940', '16.14014482416496', '16.51715192378504', '16.81881023446700', '17.38220188901755', '17.77373707650201', '18.36685734064929', '18.63265919040568', '19.11929921023203', '19.50444922665214', '19.62195346262337'], 'prelabel': '2-240825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.851993189335026, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 454787070293974188, 'z1': {'__RealLiteral__': 0, 'data': '0.4149877036933776', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '0.9162619668593431', 'prec': 54}, 'z3': {'__RealLiteral__': 0, 'data': '1.765825351911905', 'prec': 54}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1922.9973066774858, 'bad_primes': [3, 5, 13, 19], 'central_character': '1.1', 'conductor': 240825, 'conductor_radical': 3705, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 0, -1, -4, 3, 1, 0, 0, -1, 0, 4, 0, -1, -2, -1, -1, 0, -4, 0, 8, 3, 0, 0, 1, 4, 2, 0, -8, -5, 0, 2, 0, -1, 2, 1, 0, 0, 2, 4, 0, 0, 0, -8, 0, -1, 9, 0, -2, 0, -6, -1, 0, -12, -1, -2, 4, 0, 14, 8, -4, 7, 0, 0, -12, 2, 8, 0, 8, 3, 10, -2, 0, 1, 0, 0, -8, 0, 1, -2, 12, 4, 0, 0, 2, 0, -14, 0, 0, -8, -8, 0, 0, -5, 6, -9, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, 2, 17], 'euler19': [1, 1, 0], 'euler2': [1, 1, 2], 'euler23': [1, -8, 23], 'euler29': [1, -2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, 4, 7], 'euler71': [1, -8, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 14, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, 0, 0], [1, 4, 7], [1, 0, 11], [1, 0, 0], [1, 2, 17], [1, 1, 0], [1, -8, 23], [1, -2, 29], [1, 8, 31], [1, -2, 37], [1, -2, 41], [1, 0, 43], [1, 0, 47], [1, 6, 53], [1, -4, 59], [1, -14, 61], [1, 12, 67], [1, -8, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, 14, 89], [1, -6, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/240825/s'], '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': '2-240825-1.1-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-240825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.851993189335026, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 454787070293974188, 'z1': {'__RealLiteral__': 0, 'data': '0.4149877036933776', 'prec': 54}}
  • lfunc_instances • Show schema
    {'Lhash': '454787070293974188', 'Lhash_array': ['454787070293974188'], 'factors': ['2-240825-1.1-c1-0-12'], 'label': '2-240825-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/240825/s'}