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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -3, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 1, 'Lhash': '38626032912181628', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 202.75614081243526, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '25392.1', 'coefficient_field': '1.1.1.1', 'conductor': 25392, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 3, 5], [1, -4, 7], [1, 0, 11], [1, 1, 13], [1, 2, 17], [1, 0, 19], [1], [1, 1, 29], [1, 8, 31], [1, 6, 37], [1, 5, 41], [1, -12, 43], [1, -12, 47], [1, -9, 53], [1, -8, 59], [1, 11, 61], [1, 12, 67], [1, 0, 71], [1, 13, 73], [1, -12, 79], [1, -12, 83], [1, 15, 89], [1, 3, 97]], 'gamma_factors': [[], [0]], 'index': 24, 'label': '2-25392-1.1-c1-0-24', 'leading_term': '5.99789993182', '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/25392/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.410796552099423, 2.277810773225974, 2.110962599892213, 0.8254893430551593, -0.9153725780581399, -1.927318765618691, -1.394880263220657, 0.2572664358973236, 1.481407494300922, 0.927028388108655, -1.139464334263136, -2.88101282141185, -2.669655314736954, -0.8592907629659777, 0.5497815127253598, 0.2326711746005734, -0.8287568888564047, -0.6259609638799011, 1.020860363360671, 1.807002848620799, -0.1081503049704814, -3.035400888159433, -3.011806401767272, 1.400315890252996, 6.701236081200453, 8.05113252402919, 4.79013719651302, 0.8671600003391392, -0.3177794127527294, 0.3337514031302412, 0.0805108210444198, -1.181430028120462, -1.274841264900242, 0.05725533842405626, 0.3744134978773002, -1.082495093921673, -1.125696545391273, 2.794517686874573, 7.674231168074667, 8.112841895186518, 3.826729362262444, 0.1880402605893316, 0.5605607657674775, 2.043826632271617, 0.9596372272475371, -1.174433931810531, -0.913506912577613, 0.6415743090643766, -0.2650972092543641, -2.849375963529741, -2.25174820023092, 2.183833253739298, 4.866117978115452, 2.433952275105364, -1.027057710943735, -0.7572460668507149, 1.420362866673639, 1.265206390616558, -0.4714298584270683, -0.4711878274909629, 0.4152393002698677, -0.7147602194581172, -2.17159614451413, -0.2421360367193701, 2.925189779303354, 1.790395422482498, -2.514859411949948, -2.987154512893165, 1.477920656129722, 3.937531385221122, 1.241239915453781, -1.011738550910194, 1.036155474194052, 2.944828399508353, 0.8258686885440673, -1.591726805296784, -0.5158627633289316, 0.9710717911410497, -0.3802060983271874, -1.637383183382717, -0.1460025253845609, 0.9652100654154364, -0.2647328113124502, 0.06040852954606501, 3.354187782389618, 4.019353020472467, -0.2530922284779236, -2.843531124331276, 0.09515620459067291, 2.076934563335945, -1.860553980765559, -5.828616503652122, -3.885735520915757, -0.1326730886384231, 0.2168011233021768, -0.2373705396387112, 1.178823173900666, 1.034594024629917, -1.564866681884179, -1.198066681634853, 2.797932351675657, 3.274222328360944, -1.418069676696454, -3.688668153014942, -0.6559944409557277, 1.393585727960681, -0.2370364740311199, -0.94951068176429, 0.3398463595646686, 0.1507412423069504, -0.2676699618081201, 1.914521836472946, 1.991091224005206, -4.183208191239204, -9.00536090047117, -4.851809148932338, 1.18776838613841, -0.5421445228015248, -5.312978476912781, -4.16074587567907], 'positive_zeros': ['1.116941615575991', '1.963518892832839', '2.623836491234191', '3.620843231583774', '4.052646973934307', '4.607198198408520', '5.240992253607260', '5.937154564360496', '7.102895240398673', '7.384367280524296', '7.768359751258034', '8.488952215236347', '8.831911871172777', '9.350039054432032', '10.53623253728547', '10.64906720431992', '11.34942650541755', '11.87973955569373', '12.22127316193771', '12.88764517223860', '13.65464613749870', '14.08224958676795', '14.67196158411438', '15.10415099625356', '15.40071468980695', '16.01693924466184', '16.60384544950140', '17.17596978211524', '17.84012834591541', '18.16394230768173', '18.81296605950178', '19.30886865907216', '19.70513986297520'], 'prelabel': '2-25392-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.239246497354952, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 38626032912181628, 'z1': {'__RealLiteral__': 0, 'data': '1.116941615575991', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.963518892832839', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.623836491234191', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 202.75614081243526, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 25392, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -3, 0, 4, 0, 1, 0, 0, 0, -1, 0, -3, 0, -2, 0, 0, 0, 4, 0, 0, 0, 4, 0, 1, 0, -1, 0, -8, 0, 0, 0, -12, 0, -6, 0, -1, 0, -5, 0, 12, 0, -3, 0, 12, 0, 9, 0, -2, 0, 9, 0, 0, 0, 0, 0, 8, 0, -11, 0, 4, 0, 3, 0, -12, 0, 0, 0, 0, 0, -13, 0, 4, 0, 0, 0, 12, 0, 1, 0, 12, 0, 6, 0, -1, 0, -15, 0, -4, 0, -8, 0, 0, 0, -3, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 1, 29], 'euler3': [1, -1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 6, 37], 'euler41': [1, 5, 41], 'euler43': [1, -12, 43], 'euler47': [1, -12, 47], 'euler5': [1, 3, 5], 'euler53': [1, -9, 53], 'euler59': [1, -8, 59], 'euler61': [1, 11, 61], 'euler67': [1, 12, 67], 'euler7': [1, -4, 7], 'euler71': [1, 0, 71], 'euler73': [1, 13, 73], 'euler79': [1, -12, 79], 'euler83': [1, -12, 83], 'euler89': [1, 15, 89], 'euler97': [1, 3, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 3, 5], [1, -4, 7], [1, 0, 11], [1, 1, 13], [1, 2, 17], [1, 0, 19], [1, 0, 0], [1, 1, 29], [1, 8, 31], [1, 6, 37], [1, 5, 41], [1, -12, 43], [1, -12, 47], [1, -9, 53], [1, -8, 59], [1, 11, 61], [1, 12, 67], [1, 0, 71], [1, 13, 73], [1, -12, 79], [1, -12, 83], [1, 15, 89], [1, 3, 97]], 'index': 24, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25392/m'], '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': '2-25392-1.1-c1-0-24', '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': '2-25392-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.239246497354952, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 38626032912181628, 'z1': {'__RealLiteral__': 0, 'data': '1.116941615575991', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '38626032912181628', 'Lhash_array': ['38626032912181628'], 'label': '2-25392-1.1-c1-0-24', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25392/m'}