-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '225164621029405132', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 740.5006881845461, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '92736.1', 'coefficient_field': '1.1.1.1', 'conductor': 92736, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1, -1], [1, 6, 11], [1, -3, 13], [1, 0, 17], [1, 0, 19], [1, 1], [1, 3, 29], [1, 7, 31], [1, 8, 37], [1, -11, 41], [1, 4, 43], [1, 1, 47], [1, -4, 53], [1, -12, 59], [1, -6, 61], [1, 12, 67], [1, -5, 71], [1, -15, 73], [1, 4, 79], [1, 0, 83], [1, -12, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 76, 'label': '2-92736-1.1-c1-0-76', 'leading_term': '5.85382964169', '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/92736/cy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.284601028966363, 1.566528261865644, 0.3263031934623469, -1.835061335164805, -3.271536425682771, -2.685854324336139, -0.6948123238842195, 0.4897220617246544, -0.4807925356584876, -2.210791977107643, -2.037947485511257, 0.4340431252617347, 2.425428464000433, 1.553138326130392, -0.6487763024068973, -0.6042564884028561, 2.10580885352201, 3.820080358517711, 2.058592911969906, -0.7416793098543129, -1.043845415547533, 0.2306229925683869, -0.4318376912654706, -2.641852916505143, -2.149623796342334, 1.848728886904671, 4.408020793600685, 2.312329278768619, -0.7920920333063509, -0.5520887543328333, 1.096733092283808, 0.2330015401141003, -1.530169898851896, -0.3747712006892294, 1.740804693818046, 0.1053929440648794, -3.531206592659671, -3.205325571057176, 0.6470797985570352, 1.825952784841396, -0.537329040652371, -1.100067258440421, 1.110955282458958, 1.469755869187558, -0.1062135463046157, 1.327448971095349, 4.968465606404784, 4.46244997322757, 0.0713179196753903, -1.242013491209164, 1.275699817444891, 1.597664712513251, -0.6625774829137309, -0.3858793895373245, 1.321887700504397, -0.739883947259436, -3.959036964310109, -2.17869887686387, 1.583454442225331, 0.72902208648821, -1.991024361984796, -0.8677643696055352, 1.075367181211885, -0.2262321524086065, -0.5973988600757277, 2.226531646628834, 1.829592535057782, -3.507483268578683, -5.560682212333262, -1.778191311176175, 0.4845194194137903, -0.6629836455760081, 0.04368647609448481, 1.454096251095432, -0.8931122505818474, -2.717883458155522, 0.4254345005476371, 2.080634293534225, -2.038393227529942, -4.220434698736501, -0.4873998579515759, 1.827767240251143, 0.1235662992413918, -0.05679849452034113, 0.5263974029271696, -2.215140785000029, -3.361471968756043, 0.8409277157876414, 2.519519705211673, -1.975033497444743, -3.901141340195737, -0.5511048173904858, 0.4305848619604434, -1.213947116452497, 0.13336800255312, 1.364484048512438, -0.8639656596813069, -0.2113614746754476, 4.250469608568021, 3.485534555697901, -1.964245440044206, -2.628647586596025, 0.113363312031141, -0.0947878382434379, 0.5549133164992135, 4.245854589735766, 3.844750644637802, -0.006304611232177945, 0.9697495787419264, 3.599997515019566, 0.780903798548326, -1.89285705392034, 0.1732212955365972, 0.3222517869682403, -1.988037889466834, -0.05667670916606295, 2.337729196311975, -0.4890962982855291, -1.779785918953224, 1.249087384411385], 'positive_zeros': ['0.7909625372316762', '1.849606743316262', '2.176174915150045', '2.961996659186902', '3.666058467337541', '4.070344813433631', '4.919564264808666', '5.441792569995536', '5.687386088834959', '6.395719214445798', '7.165437389057454', '7.571918706494403', '8.027209754329751', '8.535986045783712', '9.007188522105184', '9.706250971058211', '10.19698378136729', '10.63235819189146', '11.22191456307445', '11.36585767024683', '12.25462261889159', '12.63370891330749', '13.17012204823442', '13.54604270464348', '13.94959557903055', '14.62565684855359', '15.05634186844584', '15.58048516422685', '15.97154599218292', '16.31588055656482', '16.84682552055840', '17.63030787345634', '17.87606803465523', '18.24465720733296', '18.68472494928812', '19.22408443077738', '19.64850287846190'], 'prelabel': '2-92736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.212142293184968, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 225164621029405132, 'z1': {'__RealLiteral__': 0, 'data': '0.7909625372316762', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.849606743316262', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.176174915150045', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 740.5006881845461, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 92736, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 1, 0, 0, 0, -6, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, -5, 0, 0, 0, -3, 0, -7, 0, 0, 0, 0, 0, -8, 0, 0, 0, 11, 0, -4, 0, 0, 0, -1, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 12, 0, 6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 5, 0, 15, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 3, 0, 0, 0, 0, 0, -14, 0, 0, 0], 'euler11': [1, 6, 11], 'euler13': [1, -3, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, 7, 31], 'euler37': [1, 8, 37], 'euler41': [1, -11, 41], 'euler43': [1, 4, 43], 'euler47': [1, 1, 47], 'euler5': [1, 0, 5], 'euler53': [1, -4, 53], 'euler59': [1, -12, 59], 'euler61': [1, -6, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -5, 71], 'euler73': [1, -15, 73], 'euler79': [1, 4, 79], 'euler83': [1, 0, 83], 'euler89': [1, -12, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, -1, 0], [1, 6, 11], [1, -3, 13], [1, 0, 17], [1, 0, 19], [1, 1, 0], [1, 3, 29], [1, 7, 31], [1, 8, 37], [1, -11, 41], [1, 4, 43], [1, 1, 47], [1, -4, 53], [1, -12, 59], [1, -6, 61], [1, 12, 67], [1, -5, 71], [1, -15, 73], [1, 4, 79], [1, 0, 83], [1, -12, 89], [1, 14, 97]], 'index': 76, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/92736/cy'], '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': '2-92736-1.1-c1-0-76', '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': '2-92736-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.212142293184968, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 225164621029405132, 'z1': {'__RealLiteral__': 0, 'data': '0.7909625372316762', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '225164621029405132', 'Lhash_array': ['225164621029405132'], 'label': '2-92736-1.1-c1-0-76', 'type': 'ECQ', 'url': 'EllipticCurve/Q/92736/cy'}