Formats: - HTML - YAML - JSON - 2026-09-20T17:22:29.905337
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '2155240008598704178', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 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, 0, 2], [1, -1], [1], [1, -1, 7], [1, -1, 11], [1], [1, -3, 17], [1, -1], [1, -5, 23], [1, 2, 29], [1, 2, 31], [1, 7, 37], [1, -5, 41], [1, 6, 43], [1, -4, 47], [1, 1, 53], [1, -4, 59], [1, -1, 61], [1, -16, 67], [1, -1, 71], [1, 6, 73], [1, -13, 79], [1, -6, 83], [1, 9, 89], [1, 1, 97]], 'gamma_factors': [[], [0]], 'index': 25, 'label': '2-240825-1.1-c1-0-25', 'leading_term': '2.92165652033', '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/bl', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 7}, 'plot_values': [2.921656520326564, 2.044743807417177, 0.04914365643350456, -1.424044067401254, -0.9797543047736845, 0.7789764594722877, 1.403512404799029, -0.4790076227234397, -2.831575733953985, -2.337359180980024, 0.978883307053757, 3.254955679522352, 2.007613519869073, -0.3333357088040709, -0.3619184374921465, 0.8785125668513026, 0.06728931974830216, -2.145324274472139, -2.026846185460203, 0.3117633925482039, 0.8152663212640007, -0.7418213385772938, 0.1877674181019364, 3.777211432804864, 3.67974211122789, -1.869634221263741, -5.304649468752913, -1.865094086092659, 2.255283567903569, 0.9419613991483387, -1.712736230127823, -0.3510219151170898, 1.871471622784884, 0.9339683662207265, -0.0852639499072761, 1.367365357055364, 1.75073221824765, -0.1162073826014385, -0.2331190785315139, 0.8926589943923592, -1.264690487618649, -3.93643359414499, -1.349971836345272, 1.862935267248862, -1.359856619271399, -4.98659517966589, -0.8539839970717676, 4.423514320519872, 2.25264957398973, -1.390785529231261, 0.5440412324595095, 2.59731693882844, 0.5837757797455874, 0.03414011305719313, 2.228596543285744, 1.743583670286051, -0.3398854527656558, 0.2106699273404317, 0.4125254533693832, -1.331685834345776, -0.2822938704280311, 1.477873634511006, -2.472971746980462, -6.169864365890914, -1.616240816143751, 2.794042337183231, -1.063155501971856, -4.276929497337163, -1.146189074761916, -0.1017708443029173, -2.589683509385058, -1.007153110036784, 1.921472996636754, 0.1614458798564908, -1.091653078206815, 1.011437127344995, 0.6165008323979116, -0.8366688900554295, 1.279961929116669, 0.9616471705688229, -3.987606163791264, -4.140171903170216, 0.2633178973714062, -0.1244143962718721, -2.098759495659139, 0.2638173253244473, 0.4429920802658932, -2.870749330370051, -1.584949299764552, 1.10810301408251, -1.387648827580507, -2.350678475148705, 0.6821920794524226, -0.4899598860849996, -3.077963568579772, -0.2797541225050299, 0.5192767668945665, -3.437450048914102, -2.338470172225073, 1.554706545995881, -0.4554472892399654, -1.718989383337607, 2.144799836210389, 2.1158020302361, -1.01814162557558, 0.4892420386194553, 1.834386502642297, -0.1021134444169023, 0.8534613271147591, 2.231509449736751, -0.06211615190313331, -0.3245632464580595, -0.1357994915067069, -4.336487476625771, -3.347855688454922, 4.391390402800106, 3.690212112229879, -2.703705064732157, -0.2213672284676779, 3.447064786622316, -0.851759079423462], 'positive_zeros': ['0.5060113864412147', '1.142289774931878', '1.704673805350137', '2.432810711286085', '3.201785086061856', '3.567064303370717', '4.007953894441329', '4.714337510277470', '5.129621845568800', '5.483694060424407', '6.175570620388284', '6.838079683372196', '7.319154380736653', '7.780140545280564', '8.404459974064436', '8.534394734879220', '9.232826022591759', '9.541130161188034', '9.904102436446778', '10.57397242321670', '10.93474894209518', '11.53085010503766', '12.11915874226360', '12.46108075320747', '13.07263404563425', '13.24444343867722', '13.93758019708421', '14.20978985323662', '14.56365346592540', '15.02522829284954', '15.38627317146396', '16.05966979026711', '16.45420441989438', '17.10160916344253', '17.23553200152969', '17.81455188167295', '18.26388849113040', '18.63730605600145', '19.06888264529572', '19.38130829195214', '19.80595795132024'], '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': 2155240008598704178, 'z1': {'__RealLiteral__': 0, 'data': '0.5060113864412147', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '1.142289774931878', 'prec': 54}, 'z3': {'__RealLiteral__': 0, 'data': '1.704673805350137', '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, 0, 1, -2, 0, 0, 1, 0, 1, 0, 1, -2, 0, 0, 0, 4, 3, 0, 1, 0, 1, 0, 5, 0, 0, 0, 1, -2, -2, 0, -2, 0, 1, 0, 0, -2, -7, 0, 0, 0, 5, 0, -6, -2, 0, 0, 4, 4, -6, 0, 3, 0, -1, 0, 0, 0, 1, 0, 4, 0, 1, 0, 1, -8, 0, 0, 16, -6, 5, 0, 1, 0, -6, 0, 0, -2, 1, 0, 13, 0, 1, 0, 6, -2, 0, 0, -2, 0, -9, 0, 0, -10, -2, 0, 0, 0, -1, 0, 1, 0], 'euler11': [1, -1, 11], 'euler13': [1, 0, 0], 'euler17': [1, -3, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 2], 'euler23': [1, -5, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 2, 31], 'euler37': [1, 7, 37], 'euler41': [1, -5, 41], 'euler43': [1, 6, 43], 'euler47': [1, -4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 1, 53], 'euler59': [1, -4, 59], 'euler61': [1, -1, 61], 'euler67': [1, -16, 67], 'euler7': [1, -1, 7], 'euler71': [1, -1, 71], 'euler73': [1, 6, 73], 'euler79': [1, -13, 79], 'euler83': [1, -6, 83], 'euler89': [1, 9, 89], 'euler97': [1, 1, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, 0, 0], [1, -1, 7], [1, -1, 11], [1, 0, 0], [1, -3, 17], [1, -1, 0], [1, -5, 23], [1, 2, 29], [1, 2, 31], [1, 7, 37], [1, -5, 41], [1, 6, 43], [1, -4, 47], [1, 1, 53], [1, -4, 59], [1, -1, 61], [1, -16, 67], [1, -1, 71], [1, 6, 73], [1, -13, 79], [1, -6, 83], [1, 9, 89], [1, 1, 97]], 'index': 25, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/240825/bl'], '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-c1-0-25', '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': 2155240008598704178, 'z1': {'__RealLiteral__': 0, 'data': '0.5060113864412147', 'prec': 54}}
  • lfunc_instances • Show schema
    {'Lhash': '2155240008598704178', 'Lhash_array': ['2155240008598704178'], 'factors': ['2-240825-1.1-c1-0-25'], 'label': '2-240825-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/240825/bl'}