-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': -2, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '1953580146781710095', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [-1.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2739.4836374254824, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [7, [1, -1]], [17, [1, 1]], [31, [1]]], 'bad_primes': [3, 7, 17, 31], 'central_character': '343077.1', 'coefficient_field': '1.1.1.1', 'conductor': 343077, 'conductor_radical': 11067, 'degree': 2, 'euler_factors': [[1, 0, 2], [1, -1], [1, -1, 5], [1, -1], [1, -5, 11], [1, -5, 13], [1, 1], [1, 5, 19], [1, -1, 23], [1, -6, 29], [1], [1, 4, 37], [1, -7, 41], [1, -7, 43], [1, -6, 47], [1, 6, 53], [1, -14, 59], [1, 0, 61], [1, 12, 67], [1, -4, 71], [1, 6, 73], [1, -6, 79], [1, -6, 83], [1, 12, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 11, 'label': '2-343077-1.1-c1-0-11', 'leading_term': '4.08341468148', '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': 0, 'origin': 'EllipticCurve/Q/343077/l', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.083414681479307, 2.98624509304651, 0.4634627192526654, -1.545783969419369, -1.494236129042054, -0.1513830819911086, -0.01693171282428921, -1.893131842691082, -3.170650277820531, -1.313251377436371, 1.779975967082589, 1.761665710829311, -1.683159084168455, -3.949487185960391, -2.424469891288748, -0.1699133193699582, -0.1012770106973742, -0.1185961430261715, 1.738805494499488, 2.171075362738705, -1.364314173144306, -4.313029972008629, -2.146174437443756, 1.039899244097835, -0.2650358524204242, -2.643950764157768, -0.8675109674436905, 0.869421377128826, -3.161663744375968, -7.748530591055512, -5.325612829960154, 0.07964652096037801, 0.718452852849565, -1.297407536038615, -0.7070093581678681, 0.4610252913446161, -0.2386784044730637, -0.01352117185452528, 0.7110009428860397, -1.985120402094776, -4.815404476074363, -2.379336081494423, 0.2555481314488269, -2.283694714012399, -2.685995821135317, 3.706714740596692, 6.802111990305981, 1.777536484727073, -0.5863667758475468, 3.603778358346111, 4.388213751165911, 0.09145643578238263, -0.8318772888845208, 1.044488680044467, 0.0126539109118265, -1.139472421346799, 0.1235982542896756, 0.1353203376676869, 0.04500787655144502, 2.494207247165039, 1.933467440789614, -2.279256981549971, -0.9486350315960643, 3.709060947037655, 0.5210780289093196, -4.988022777331702, -1.442878082057403, 3.455541663561915, 0.5992691779759307, -2.082178409553071, -0.2324329260335773, -0.1336466198456278, -0.05195668553546022, 3.543963908179142, 3.67911643877317, -0.5041961342406531, -0.7642426803141182, 0.8409007812710722, -0.1884104381462354, 2.274852738092965, 6.870643137280452, 3.718552499238055, -1.894371653222579, -0.592309121779716, 0.8113845483675366, -1.543877210662123, -0.595299831054173, 0.9285517285273828, -1.795589676969084, -1.374660648535699, 2.313422624502414, 0.9781388889855019, -0.1094068555358012, 3.874448978792327, 3.602041874389252, 0.01086047417205292, 2.218521250652407, 2.823716232688427, -3.26505117049911, -4.14590145649474, 0.7097116427472719, 0.9691373829130486, -0.02154148662786398, 0.7220379122801364, -2.660872700272979, -5.062909682655266, -1.164183811112678, 0.2083568494096065, -1.768930619685847, -0.08497133101124138, 0.59099935460945, -1.171305434664327, 0.5675327153364625, 0.1168489930579616, -3.179748579163096, 2.720153182380779, 9.906350546407552, 3.532979841289711, -3.477621159150731, -0.6500816080570047, -0.07632068551142626], 'positive_zeros': ['0.5450602540224040', '1.286593102952107', '1.495889860877595', '2.347496360418880', '2.890685165453940', '3.793101755051092', '3.956949259173543', '4.275529296501990', '4.922538837411543', '5.638997991560736', '5.978165253564110', '6.570484287178175', '6.844769694947719', '7.744653592505170', '8.081902539742749', '8.607057766337573', '8.934523460295056', '9.252840884158408', '9.608287963246502', '10.42600576836003', '10.56526422761747', '11.12261879110299', '11.84024253844277', '12.05323152096152', '12.75621884828556', '13.09900349648718', '13.50149389144674', '13.97591775050181', '14.28762930451514', '14.49190333699143', '15.11078101888169', '15.54439643999368', '16.01847797131642', '16.55242555941108', '17.03197718342348', '17.53658861693231', '17.71978085630850', '18.00561081376364', '18.71435505255991', '19.08455380197628', '19.44775582417239', '19.59362931383154'], 'prelabel': '2-343077-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.340076780851994, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1953580146781710095, 'z1': {'__RealLiteral__': 0, 'data': '0.5450602540224040', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.286593102952107', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.495889860877595', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2739.4836374254824, 'bad_primes': [3, 7, 17, 31], 'central_character': '1.1', 'conductor': 343077, 'conductor_radical': 11067, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, -2, 1, 0, 1, 0, 1, 0, 5, -2, 5, 0, 1, 4, -1, 0, -5, -2, 1, 0, 1, 0, -4, 0, 1, -2, 6, 0, 0, 0, 5, 0, 1, -2, -4, 0, 5, 0, 7, 0, 7, -10, 1, 0, 6, 4, 1, 0, -1, -10, -6, 0, 5, 0, -5, 0, 14, -2, 0, 0, 1, -8, 5, 0, -12, 2, 1, 0, 4, 0, -6, 0, -4, 10, 5, 0, 6, 4, 1, 0, 6, -2, -1, 0, 6, 0, -12, 0, 5, -2, 0, 0, -5, 0, 8, 0, 5, 8], 'euler11': [1, -5, 11], 'euler13': [1, -5, 13], 'euler17': [1, 1, 0], 'euler19': [1, 5, 19], 'euler2': [1, 0, 2], 'euler23': [1, -1, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 0], 'euler37': [1, 4, 37], 'euler41': [1, -7, 41], 'euler43': [1, -7, 43], 'euler47': [1, -6, 47], 'euler5': [1, -1, 5], 'euler53': [1, 6, 53], 'euler59': [1, -14, 59], 'euler61': [1, 0, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -4, 71], 'euler73': [1, 6, 73], 'euler79': [1, -6, 79], 'euler83': [1, -6, 83], 'euler89': [1, 12, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 2], [1, -1, 0], [1, -1, 5], [1, -1, 0], [1, -5, 11], [1, -5, 13], [1, 1, 0], [1, 5, 19], [1, -1, 23], [1, -6, 29], [1, 0, 0], [1, 4, 37], [1, -7, 41], [1, -7, 43], [1, -6, 47], [1, 6, 53], [1, -14, 59], [1, 0, 61], [1, 12, 67], [1, -4, 71], [1, 6, 73], [1, -6, 79], [1, -6, 83], [1, 12, 89], [1, -8, 97]], 'index': 11, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/343077/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': '2-343077-1.1-c1-0-11', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-343077-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 52.340076780851994, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1953580146781710095, 'z1': {'__RealLiteral__': 0, 'data': '0.5450602540224040', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1953580146781710095', 'Lhash_array': ['1953580146781710095'], 'label': '2-343077-1.1-c1-0-11', 'type': 'ECQ', 'url': 'EllipticCurve/Q/343077/l'}