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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -2, 'Lhash': '243405158505752139', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 125.2054303693677, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '15680.1', 'coefficient_field': '1.1.1.1', 'conductor': 15680, 'conductor_radical': 70, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 1], [1], [1, -3, 11], [1, 1, 13], [1, 5, 17], [1, 6, 19], [1, 0, 23], [1, -5, 29], [1, 2, 31], [1, -4, 37], [1, 2, 41], [1, -10, 43], [1, -9, 47], [1, 6, 53], [1, 6, 59], [1, -12, 61], [1, 2, 67], [1, 0, 71], [1, 14, 73], [1, 1, 79], [1, -12, 83], [1, 0, 89], [1, 9, 97]], 'gamma_factors': [[], [0]], 'index': 51, 'label': '2-15680-1.1-c1-0-51', 'leading_term': '3.31509520309', '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/15680/bh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7635685397802208, 1.126635762711464, 0.7200539551279465, -0.5439061987077505, -2.18384071907366, -3.224157053422439, -2.805427826238432, -0.9817506402747921, 1.024766150577722, 1.594668471627336, 0.09313721841915087, -2.353538939665915, -3.645500076634622, -2.601562466411055, -0.1796602295481361, 1.390678819491979, 0.9035510949299292, -0.5008280586135381, -0.6080538268744757, 1.250397654834535, 3.266905302604001, 3.218206253263721, 1.189942248943148, -0.4593347572111714, -0.05999936544295581, 1.191469339523479, 0.8582955197692504, -1.226214764045825, -2.34673403657399, -0.4306508337134158, 2.825913928169525, 3.763488324654033, 1.485374343553038, -0.913327521003569, -0.6130139010364323, 0.937146157369951, 0.1102632538061429, -3.420694480628346, -5.712567272970927, -3.835346272801096, -0.004504996022242455, 1.461367604458417, -0.02822324647499489, -1.191392406382238, -0.2596391220427376, 0.6051270653916391, -0.5827051572535038, -2.013289903914355, -1.154915294229063, 0.5272048711822571, -0.4532462031348083, -3.512227288745812, -3.995030409822907, -0.2626176788836391, 3.185024597682278, 2.164947937436837, -0.931845707292287, -1.122108181365999, 1.24982934547302, 1.483856880110336, -1.360202108870245, -2.819978256086762, -0.587869978615609, 1.578965861389713, 0.2114224394159496, -2.188854876054004, -1.732956081071761, 0.3187930902700221, 0.476100509807762, -0.353152572573039, 1.076004131458191, 3.349366876682644, 1.945633730456976, -2.48660951039505, -4.127078526498978, -1.284136052447898, 1.025938574674479, -0.09746857547893412, -0.9108253095972882, 1.225160696750469, 2.397444456750536, -0.450295144215322, -2.794184237001719, 0.278736351997087, 5.146189991017281, 5.225514411816294, 1.529751898003174, -0.1381798355743543, 0.6077802934397629, -0.3326736973761996, -2.662452466315153, -2.40138038398593, -0.1332830761707283, 0.06927561415447032, -1.007556725846178, 0.7880591808967307, 3.954129332313652, 3.114881133104326, -0.6356349893310852, -1.035563988504783, 1.745018926399758, 1.329628869594202, -2.504326167453953, -2.878618522658784, 1.332768621833802, 3.131315269519351, 0.1168489768805614, -1.743109973342183, 0.2587052255772758, 1.368073893784995, -0.344342043526181, -0.542776297615275, 1.732755837338632, 1.854537106721687, -0.6224896589949668, -0.856447881834067, 1.040310814203173, -0.07412303388856736, -3.379354333712747, -2.887394793474105], 'positive_zeros': ['0.9087992454753121', '2.112338427470954', '2.760046658424459', '3.769334643274700', '4.403737694432140', '4.856192615940822', '5.898779760669487', '6.261817671816554', '6.864245193616678', '7.532880943023111', '8.379929753374702', '8.839838640999551', '9.260419061274222', '10.25035192269419', '10.74637683497733', '11.29574618531519', '11.66698629651409', '12.39847613731656', '12.70204511330969', '13.51419893285825', '14.16441921773535', '14.62235626543621', '15.14321347797224', '15.79778185867017', '16.26915966367854', '16.95209351175673', '17.36088352652107', '17.62277416217562', '18.36275556367272', '19.09766031251421', '19.48705707305721', '19.88399044673725'], 'prelabel': '2-15680-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.189523241379309, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 243405158505752139, 'z1': {'__RealLiteral__': 0, 'data': '0.9087992454753121', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.112338427470954', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.760046658424459', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 125.2054303693677, 'bad_primes': [2, 5, 7], 'central_character': '1.1', 'conductor': 15680, 'conductor_radical': 70, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, -2, 0, 3, 0, -1, 0, 1, 0, -5, 0, -6, 0, 0, 0, 0, 0, 1, 0, 5, 0, 5, 0, -2, 0, -3, 0, 0, 0, 4, 0, 1, 0, -2, 0, 10, 0, 2, 0, 9, 0, 0, 0, 5, 0, -6, 0, -3, 0, 6, 0, -6, 0, 12, 0, 0, 0, 1, 0, -2, 0, 0, 0, 0, 0, -14, 0, -1, 0, 0, 0, -1, 0, 1, 0, 12, 0, 5, 0, -5, 0, 0, 0, 0, 0, 2, 0, 6, 0, -9, 0, -6, 0], 'euler11': [1, -3, 11], 'euler13': [1, 1, 13], 'euler17': [1, 5, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -5, 29], 'euler3': [1, 1, 3], 'euler31': [1, 2, 31], 'euler37': [1, -4, 37], 'euler41': [1, 2, 41], 'euler43': [1, -10, 43], 'euler47': [1, -9, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, 6, 59], 'euler61': [1, -12, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, 1, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 9, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 1, 0], [1, 0, 0], [1, -3, 11], [1, 1, 13], [1, 5, 17], [1, 6, 19], [1, 0, 23], [1, -5, 29], [1, 2, 31], [1, -4, 37], [1, 2, 41], [1, -10, 43], [1, -9, 47], [1, 6, 53], [1, 6, 59], [1, -12, 61], [1, 2, 67], [1, 0, 71], [1, 14, 73], [1, 1, 79], [1, -12, 83], [1, 0, 89], [1, 9, 97]], 'index': 51, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/15680/bh'], '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': '2-15680-1.1-c1-0-51', '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': '2-15680-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.189523241379309, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 243405158505752139, 'z1': {'__RealLiteral__': 0, 'data': '0.9087992454753121', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '243405158505752139', 'Lhash_array': ['243405158505752139'], 'label': '2-15680-1.1-c1-0-51', 'type': 'ECQ', 'url': 'EllipticCurve/Q/15680/bh'}