-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 1, 'A2': 1, 'A3': 0, 'A4': 1, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 1, 'A9': 0, 'Lhash': '2230097460391852876', 'a10': [0.31622776601683794, 0], 'a2': [0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 86.95708780117438, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [5, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '10890.1', 'coefficient_field': '1.1.1.1', 'conductor': 10890, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, -1], [1, 0, 7], [1], [1, 6, 13], [1, -6, 17], [1, 0, 19], [1, -6, 23], [1, 0, 29], [1, -4, 31], [1, 2, 37], [1, -12, 41], [1, -12, 43], [1, 6, 47], [1, 6, 53], [1, 0, 59], [1, 0, 61], [1, 14, 67], [1, 0, 71], [1, 6, 73], [1, -12, 79], [1, 12, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 18, 'label': '2-10890-1.1-c1-0-18', 'leading_term': '3.82948020739', '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/10890/bz', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.829480207391737, 3.445441974724643, 2.301605976656157, 0.562821209577738, -1.250791391899914, -2.356667765057406, -2.156331005286489, -0.7410434672034251, 0.9997219650106948, 1.913212940365837, 1.474629206101336, 0.3017245222461192, -0.2900107295036131, 0.5326236898097809, 2.239438170724077, 3.309815323261668, 2.676750285316812, 0.8638083694595787, -0.460552197639907, -0.2065770091086206, 0.9512601231689228, 1.358254867536355, 0.386073151477491, -0.6888139533568434, -0.184681801026714, 1.74070793627349, 2.96144840690685, 1.879429451593634, -0.391456249725013, -1.169805868389681, 0.3249471902426077, 1.554737393107607, -0.3776175082122912, -4.682205755611068, -7.089468176530877, -4.711946071936817, 0.2500090145479413, 2.906545261169485, 1.495503074729784, -0.7592782544718637, -0.194913641759521, 2.390158487282309, 3.087684041653911, 0.5446806623111204, -2.014704345116869, -1.264619929329377, 1.62314766723984, 2.778492328498065, 1.079614326010445, -0.6989170036892239, -0.4149766255545112, 0.3373037419179785, -0.8045400397946215, -2.853806833732249, -2.877632940922566, -0.6952880375366003, 0.754650558052037, 0.04246011055696886, -0.7084326515667652, 0.2107006039886927, 0.8275664824146814, -1.177847498544623, -3.82943269029953, -3.198051957325508, 0.2639199920823627, 1.836692504772618, -0.293786449893917, -2.178899007416552, -0.6227243665839951, 1.412419210192702, -0.1301163185675301, -2.850675606769389, -0.9302527293205276, 5.208897362317147, 8.38488791709205, 5.015931780248406, 0.2050644329674214, -0.5176214113327485, 0.6427576806819635, -1.396613609102351, -5.46614447204236, -6.05397326280768, -2.474353421947768, 0.3710990785022887, 0.2342079292271952, 0.2157928800574122, 2.093804957623438, 3.007849660361189, 1.192103267026355, -0.4341461426718729, 0.3483095120107075, 0.9611394322866593, -0.8340327020932236, -2.227789885683081, -0.3818139268405878, 1.912783095215684, 0.8736879108042562, -1.534903527482416, -1.362398991205969, 0.01932087539005754, -1.014695473692445, -2.708520213831678, -0.9262415233744427, 2.227562733631459, 1.287885037653998, -2.110248400384731, -1.02781522266465, 4.312182804654166, 5.964941867592359, 1.939286307400902, -0.0957048030942549, 3.651115345264765, 6.299299237245026, 2.474296060529654, -2.399088738630203, -1.826227851204128, 1.250922246617667, 1.23540867031278, -0.3584697777970992, 0.1557920484994939, 0.6337763309758117], 'positive_zeros': ['0.8241041219040363', '1.852177541231141', '2.826321435124352', '3.141020330725166', '4.381835932564793', '4.799242686484448', '5.571722664612665', '6.029820533520251', '6.952746523493199', '7.458860056420024', '7.972998004259617', '8.986444007451215', '9.643656356170030', '10.02182744579332', '10.79131546667575', '11.36222206810950', '12.12328646745091', '12.59890196876633', '12.88256251320329', '13.83080587019365', '14.25853975733501', '14.71068467323880', '15.14160161771121', '15.98061106983294', '16.47485359521099', '17.05711153815389', '17.48951530127499', '18.04380730077514', '19.01738754562045', '19.33959004637491', '19.64125547289423'], 'prelabel': '2-10890-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.325078434049463, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2230097460391852876, 'z1': {'__RealLiteral__': 0, 'data': '0.8241041219040363', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.852177541231141', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.826321435124352', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 86.95708780117438, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 10890, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 1, 0, 0, 1, 0, 1, 0, 0, -6, 0, 0, 1, 6, 0, 0, 1, 0, 0, 6, 0, 1, -6, 0, 0, 0, 0, 4, 1, 0, 6, 0, 0, -2, 0, 0, 1, 12, 0, 12, 0, 0, 6, -6, 0, -7, 1, 0, -6, -6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 1, -6, 0, -14, 6, 0, 0, 0, 0, -6, -2, 0, 0, 0, 0, 12, 1, 0, 12, -12, 0, 6, 12, 0, 0, -6, 0, 0, 6, 0, -6, 0, 0, -10, -7, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, 6, 13], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, -1, 0], 'euler23': [1, -6, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -12, 41], 'euler43': [1, -12, 43], 'euler47': [1, 6, 47], 'euler5': [1, -1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 0, 61], 'euler67': [1, 14, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 6, 73], 'euler79': [1, -12, 79], 'euler83': [1, 12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, -1, 0], [1, 0, 7], [1, 0, 0], [1, 6, 13], [1, -6, 17], [1, 0, 19], [1, -6, 23], [1, 0, 29], [1, -4, 31], [1, 2, 37], [1, -12, 41], [1, -12, 43], [1, 6, 47], [1, 6, 53], [1, 0, 59], [1, 0, 61], [1, 14, 67], [1, 0, 71], [1, 6, 73], [1, -12, 79], [1, 12, 83], [1, 6, 89], [1, 10, 97]], 'index': 18, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10890/bz'], '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': '2-10890-1.1-c1-0-18', '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': '2-10890-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.325078434049463, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2230097460391852876, 'z1': {'__RealLiteral__': 0, 'data': '0.8241041219040363', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2230097460391852876', 'Lhash_array': ['2230097460391852876'], 'label': '2-10890-1.1-c1-0-18', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10890/bz'}