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lfunc_lfunctions • Show schema
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{'A10': 1, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': -1, 'A6': 0, 'A7': 4, 'A8': -1, 'A9': 0, 'Lhash': '1569841307310619346', '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': [1.5118578920369088, 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, -4, 7], [1], [1, -4, 13], [1, -6, 17], [1, 2, 19], [1, 6, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, -6, 41], [1, -10, 43], [1, 6, 47], [1, -6, 53], [1, 0, 59], [1, 8, 61], [1, 4, 67], [1, 6, 71], [1, 14, 73], [1, -16, 79], [1, 12, 83], [1, 0, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-10890-1.1-c1-0-20', 'leading_term': '2.07375864449', '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/n', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.073758644487012, 1.846787851013472, 1.201064698700959, 0.3191437686015765, -0.3920402958617941, -0.4557422598028389, 0.2956431203073124, 1.408819441551133, 1.938045275535924, 1.113701891025871, -0.8695389940051873, -2.689589390704162, -2.770656933715937, -0.6809806154002058, 2.194432705569692, 3.600736968035111, 2.424782066260553, -0.06698903053222394, -1.215618095110515, 0.4610708474932395, 3.613710389211682, 5.243433243620892, 3.779777279466382, 0.8506712466653829, -0.3583782576832842, 1.434417627070946, 4.158051236839002, 4.700121840113834, 2.389438571238229, -0.411443478602669, -1.2345769229204, -0.2761844380359655, 0.3966581743148473, -0.07766799760171106, -0.2924652854796534, 1.00961192685534, 2.569497870200389, 1.976339114594482, -0.8442698578022951, -3.032814014749422, -2.362819852146718, -0.2039280101331807, 0.4209991291648272, -0.918287420840667, -1.644683730383121, -0.2487186850303014, 1.323347191565902, 0.8490519591292236, -0.2077438496269994, 1.396512832319038, 5.05514777678616, 5.74818381038686, 0.6982043848138668, -5.8375327549925, -7.298174695539985, -3.227816400050531, 0.4597543635292814, -0.1812258094190712, -2.229404821084453, -1.233207107909743, 1.780157239675371, 2.287022974812797, -0.3706734096122088, -2.078617574447038, -0.6777278624604581, 0.7493295597570444, -0.7716696617321925, -3.125979056184273, -2.665082874190611, -0.1745777725279828, 0.6731326328229154, -0.5694856058148611, -0.937282400561, 0.2940596173241359, 0.3691510461830323, -1.586452120949116, -2.4953498210636, -0.7522680080497374, 0.4592559626179036, -1.52230427346421, -3.861951305776438, -2.740403860178827, 0.147613584132276, 0.6654076738825934, -0.4914691365490076, 0.2742203185234311, 1.493138468107447, -2.04544292018353, -9.22951963485337, -11.64714690150511, -5.74277753380726, 1.124348409944735, 1.454753602276432, -1.867834647281852, -1.947011509829756, 0.6730573540933278, 0.6888152684213829, -1.570096803784684, -1.156659522192478, 1.803929171732075, 2.173443018567567, -0.6257604223160836, -1.492348895077103, 1.000610488394106, 2.212817538536005, 0.1746028339200962, -1.023594363584876, 0.8952574005311761, 2.422571921541449, 1.151340635202267, -0.22514818311001, 0.1390771785198656, 0.1025102824888685, -0.6135251674683079, 1.347216152240584, 5.515176945504911, 6.022132806013587, 1.445209116593142, -1.701025662978748, 0.2786494809043643, 2.367537009551563], 'positive_zeros': ['0.8453637738747555', '1.425395506675942', '2.399759980389422', '3.308184743000544', '4.242646315437053', '4.707531393111455', '5.852079924130861', '6.092337078757644', '7.204130191603557', '7.813768943649960', '8.222043707773533', '8.588301413191471', '9.432618012834167', '10.28037300346622', '10.60203124966908', '11.28083558870901', '11.91163527003461', '12.09710592495068', '13.02465876341383', '13.94603832233303', '14.22939480995220', '14.85094759881894', '15.46934103968118', '16.08057713416091', '16.42071807319542', '17.27087790658883', '17.65057890423158', '18.19298121956670', '18.56174591514659', '19.34305879890227', '19.60151675547830'], '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': 1569841307310619346, 'z1': {'__RealLiteral__': 0, 'data': '0.8453637738747555', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.425395506675942', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.399759980389422', 'prec': 57}}
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lfunc_search • Show schema
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{'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, 4, -1, 0, 1, 0, 0, 4, -4, 0, 1, 6, 0, -2, -1, 0, 0, -6, 0, 1, -4, 0, 4, 6, 0, 8, -1, 0, -6, -4, 0, 2, 2, 0, 1, 6, 0, 10, 0, 0, 6, -6, 0, 9, -1, 0, 4, 6, 0, 0, -4, 0, -6, 0, 0, -8, -8, 0, 1, -4, 0, -4, 6, 0, 4, -6, 0, -14, -2, 0, -2, 0, 0, 16, -1, 0, -6, -12, 0, -6, -10, 0, 0, 0, 0, 16, -6, 0, 6, 2, 0, 14, -9, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, -4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 1, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -10, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, 8, 61], 'euler67': [1, 4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 6, 71], 'euler73': [1, 14, 73], 'euler79': [1, -16, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -4, 7], [1, 0, 0], [1, -4, 13], [1, -6, 17], [1, 2, 19], [1, 6, 23], [1, -6, 29], [1, -8, 31], [1, -2, 37], [1, -6, 41], [1, -10, 43], [1, 6, 47], [1, -6, 53], [1, 0, 59], [1, 8, 61], [1, 4, 67], [1, 6, 71], [1, 14, 73], [1, -16, 79], [1, 12, 83], [1, 0, 89], [1, -14, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10890/n'], '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-c1-0-20', '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': 1569841307310619346, 'z1': {'__RealLiteral__': 0, 'data': '0.8453637738747555', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1569841307310619346', 'Lhash_array': ['1569841307310619346'], 'label': '2-10890-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10890/n'}