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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '1365816740199509651', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 425.6984632558502, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]], [17, [1, -1]]], 'bad_primes': [2, 7, 17], 'central_character': '53312.1', 'coefficient_field': '1.1.1.1', 'conductor': 53312, 'conductor_radical': 238, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 4, 5], [1], [1, 3, 11], [1, 5, 13], [1, -1], [1, 6, 19], [1, -4, 23], [1, 8, 29], [1, 0, 31], [1, -8, 37], [1, -8, 41], [1, -10, 43], [1, 2, 47], [1, 3, 53], [1, 2, 59], [1, 8, 61], [1, -14, 67], [1, 7, 71], [1, -8, 73], [1, 15, 79], [1, 12, 83], [1, 1, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 49, 'label': '2-53312-1.1-c1-0-49', 'leading_term': '5.5680915573', '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': 2, 'origin': 'EllipticCurve/Q/53312/t', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.325441601602878, -1.023453790285541, -1.284831163259995, -0.145928627928004, 2.599700822632728, 5.690391518135012, 6.974034598257194, 5.276909418647453, 1.869817674653292, -0.3821947551591613, 0.1527751795426667, 2.030665893493352, 2.320343985879134, 0.1279718084641438, -2.252690736506367, -2.29969537745719, -0.6189711078010868, -0.02278110485303217, -1.398677573467607, -2.335394075275244, -0.8690434652770574, 1.073924161757826, 0.1922228458264842, -2.938581826565779, -4.04286732075052, -1.226078342086125, 2.045257059259443, 1.961905601338757, -0.1791473035150029, -0.6422173860732394, 0.4958047095232618, 0.0652904307080733, -1.827541170623761, -1.344909029259066, 1.979484947306281, 3.068206447330931, -0.6723363726654107, -4.025078907197433, -1.421464391261516, 4.120194990502455, 5.460108724904836, 2.065686141325159, -0.4730942012237743, -0.09936898407362547, -0.05282662174933166, -1.301535589624709, -0.9172604295018822, 1.192560520489628, 1.511474668941047, 0.05232970231197451, 0.3707628074866393, 1.140290569524911, -3.201717342858046, -11.08899061048124, -13.10715312260481, -6.398437277665143, 0.291122098877547, 0.5340135614907896, -1.151968247062118, 0.1469979288689691, 1.31944309908989, -0.3992024206595802, -1.063602336520226, 1.492213760214447, 2.753550900756432, 0.7462066028640496, -0.09038151800741401, 1.293846504560202, 0.1842214185376634, -2.9428608223463, -1.627631137224909, 3.547639847174656, 4.563160965568996, 0.5508285158082818, -1.216163280462537, 0.5082820594698672, 0.2860204887917605, -1.587904001642425, -0.7249573099872695, 0.4263013112200341, -2.177266639732924, -3.754782169887792, 0.1793070321233103, 2.913773310682211, -1.187874744147816, -4.752560511440712, -1.181655426855246, 2.909300846622706, 1.116197088670271, -1.562601002478126, -0.6519458310265668, 0.09852743600047278, -0.8851979134584657, -0.3841119365388427, 0.3063087707050537, -1.603227784956678, -2.205257079819661, 0.2189653540242633, -1.597294755591315, -8.741261060586677, -9.920845177364738, -1.970696080068489, 3.217697806314279, 0.9123914727157445, 0.1589303960771723, 3.438000636264489, 3.358390875497667, 0.08899017856802853, -0.09934649674555406, 1.12047627155973, 0.06768567518483909, 0.3717128491920092, 2.898227018541165, 2.058660740273651, -0.7763504848015863, 0.7097934049140876, 2.898926707169095, -0.05804360438618804, -2.043199180382886, 1.874855628639734], 'positive_zeros': ['1.017518343482637', '2.427864208599047', '2.726251095400751', '3.511267501004365', '4.393206195874410', '4.489025600816516', '5.342411933902495', '5.768124240941405', '6.578635597773967', '7.225805870205977', '7.639030965605177', '8.009622777933602', '8.610176929211600', '9.215445116417312', '9.812890306345039', '10.66617991779924', '11.03210899851035', '11.23488137318044', '11.86039971054657', '12.51375290740198', '12.67225757714595', '13.11263989619804', '14.23101227360606', '14.56078423670992', '14.98315409147031', '15.45462973825735', '15.87461565375626', '16.60405528938385', '16.77336179575211', '17.26474667031787', '17.83150995107343', '18.53630441087428', '18.92990605872205', '19.28578848259505', '19.84103510049585'], 'prelabel': '2-53312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.63246139596171, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1365816740199509651, 'z1': {'__RealLiteral__': 0, 'data': '1.017518343482637', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.427864208599047', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.726251095400751', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 425.6984632558502, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 53312, 'conductor_radical': 238, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -4, 0, 0, 0, -2, 0, -3, 0, -5, 0, 4, 0, 1, 0, -6, 0, 0, 0, 4, 0, 11, 0, 5, 0, -8, 0, 0, 0, 3, 0, 0, 0, 8, 0, 5, 0, 8, 0, 10, 0, 8, 0, -2, 0, 0, 0, -1, 0, -3, 0, 12, 0, 6, 0, -2, 0, -8, 0, 0, 0, 20, 0, 14, 0, -4, 0, -7, 0, 8, 0, -11, 0, 0, 0, -15, 0, 1, 0, -12, 0, -4, 0, 8, 0, -1, 0, 0, 0, 0, 0, 24, 0, -18, 0, 6, 0], 'euler11': [1, 3, 11], 'euler13': [1, 5, 13], 'euler17': [1, -1, 0], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 3], 'euler31': [1, 0, 31], 'euler37': [1, -8, 37], 'euler41': [1, -8, 41], 'euler43': [1, -10, 43], 'euler47': [1, 2, 47], 'euler5': [1, 4, 5], 'euler53': [1, 3, 53], 'euler59': [1, 2, 59], 'euler61': [1, 8, 61], 'euler67': [1, -14, 67], 'euler7': [1, 0, 0], 'euler71': [1, 7, 71], 'euler73': [1, -8, 73], 'euler79': [1, 15, 79], 'euler83': [1, 12, 83], 'euler89': [1, 1, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 4, 5], [1, 0, 0], [1, 3, 11], [1, 5, 13], [1, -1, 0], [1, 6, 19], [1, -4, 23], [1, 8, 29], [1, 0, 31], [1, -8, 37], [1, -8, 41], [1, -10, 43], [1, 2, 47], [1, 3, 53], [1, 2, 59], [1, 8, 61], [1, -14, 67], [1, 7, 71], [1, -8, 73], [1, 15, 79], [1, 12, 83], [1, 1, 89], [1, 18, 97]], 'index': 49, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/53312/t'], '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': '2-53312-1.1-c1-0-49', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-53312-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.63246139596171, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1365816740199509651, 'z1': {'__RealLiteral__': 0, 'data': '1.017518343482637', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1365816740199509651', 'Lhash_array': ['1365816740199509651'], 'label': '2-53312-1.1-c1-0-49', 'type': 'ECQ', 'url': 'EllipticCurve/Q/53312/t'}