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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': 1, 'A7': -1, 'A8': -1, 'A9': 1, 'Lhash': '1124966900825041005', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 92.22721433457889, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '11550.1', 'coefficient_field': '1.1.1.1', 'conductor': 11550, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1], [1, 1], [1, -1], [1, -2, 13], [1, -2, 17], [1, 6, 19], [1, 0, 23], [1, 0, 29], [1, -8, 31], [1, 2, 37], [1, 4, 41], [1, 4, 43], [1, 2, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, 2, 67], [1, -4, 71], [1, 10, 73], [1, -10, 79], [1, 12, 83], [1, -6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 33, 'label': '2-11550-1.1-c1-0-33', 'leading_term': '2.7564836294', '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/11550/g', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.6462426994031287, 1.02601857118468, 0.8835820985333346, 0.1481870772808424, -0.8483610581773476, -1.400314008277831, -0.8571032305083273, 0.757355946135414, 2.470434020440917, 2.880413135337083, 1.296549745729664, -1.403464908182262, -3.166763676213398, -2.414118771205841, 0.3714388631292279, 2.755196071242443, 2.427526835334427, -0.5194451300499406, -3.454348721762539, -3.647901061933929, -0.9918166800169832, 1.892063363121489, 2.419253323986275, 0.7251923427302289, -0.7705864045853655, -0.4150817295353339, 0.6912559382215097, 0.2597029073854616, -2.008441503270359, -3.773986026422605, -2.969869631891464, -0.5698551403457223, 0.5518279254828328, -0.6485332813157901, -2.019998111617727, -1.176550259128531, 1.187858204760476, 2.25245508268226, 1.015364468943006, -0.3759329684480596, 0.1414704540511504, 1.494755393133418, 1.223200886558059, -0.5444324080663095, -1.08335682812727, 0.6525176064156356, 2.068524114000783, 0.8005573120165793, -1.250845774612045, -0.4455173082216998, 2.690166498493375, 3.471723389842517, 0.01908301204426508, -3.007554225595661, -0.4576145459710871, 5.534916706954562, 7.776126727986458, 3.756946390853535, -1.017985386844938, -0.9358080908316078, 2.280241810600564, 3.163105910237301, 0.8297149163658979, -0.6943483750278348, 0.4816116907348195, 1.559215032455698, 0.3943238992564081, -0.9976292560948788, -0.4954900770250136, 0.2066369185534662, -1.102534724872391, -2.733649571778174, -1.820716660274617, 0.4871235023080295, 0.881725991228779, -0.2468422989462258, 0.3340243647368637, 2.295749189592093, 1.656918468410799, -1.906978135299928, -3.358171088385003, -0.3783833309221901, 2.350654448281863, 0.8265702918008471, -1.435083918317806, 0.3578206228154622, 3.506173349918974, 2.21801793070997, -2.082184239658145, -2.78771591853845, 0.6858713808667494, 2.147556151526593, -0.4070608502936797, -1.705831307456101, 0.701011162405789, 1.731403075781127, -1.851200322177625, -5.10822653496049, -3.329821955856041, -0.001813652161735143, -0.1493691679355803, -1.642475318161002, -0.1277741731356358, 2.405355637245403, 1.584135080456208, -0.8562271666082862, -0.3371569085165313, 2.007205471049806, 1.773304500828197, -0.4076024669219369, -0.6403728519872606, 0.6128180848165934, 0.2402500203716623, -0.6563027129372895, 0.7757969616868322, 2.450482040750689, 0.9038447995771078, -1.447935195948258, -0.7020281900736953, 0.5871601371890441], 'positive_zeros': ['1.037792526351240', '1.896239649800356', '2.872324816158318', '3.719932555817605', '4.462733921498354', '5.325036702716607', '6.093887159600340', '6.585064345758375', '7.037676780045465', '8.072808405923134', '8.404256130409997', '9.126336719032790', '9.902270206968222', '10.22307481092352', '10.92396846026270', '11.42511589185533', '12.08313390037835', '12.54016858321571', '13.25108620966529', '13.77083109645647', '14.67778362757503', '15.07800780719029', '15.83669999963331', '16.18103595326756', '16.80357278273145', '17.36539404648639', '17.58325855536509', '18.43889987878633', '18.93456214313352', '19.19802116796067', '19.87390292608272'], 'prelabel': '2-11550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.603500108532247, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1124966900825041005, 'z1': {'__RealLiteral__': 0, 'data': '1.037792526351240', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.896239649800356', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.872324816158318', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.22721433457889, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 11550, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -1, -1, 1, 0, 1, -1, 2, 1, 0, 1, 2, -1, -6, 0, 1, -1, 0, 1, 0, -2, -1, -1, 0, 0, 8, -1, -1, -2, 0, 1, -2, 6, -2, 0, -4, -1, -4, 1, 0, 0, -2, -1, 1, 0, -2, 2, -6, 1, 0, 1, 6, 0, 0, 0, 14, -8, -1, 1, 0, 1, -2, 2, 0, 0, 4, -1, -10, 2, 0, -6, -1, 2, 10, 0, 1, 4, -12, 1, 0, 4, 0, -1, 6, 0, -2, 0, -8, 2, 0, 1, -10, -1, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 6, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 4, 41], 'euler43': [1, 4, 43], 'euler47': [1, 2, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -14, 61], 'euler67': [1, 2, 67], 'euler7': [1, 1, 0], 'euler71': [1, -4, 71], 'euler73': [1, 10, 73], 'euler79': [1, -10, 79], 'euler83': [1, 12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -2, 13], [1, -2, 17], [1, 6, 19], [1, 0, 23], [1, 0, 29], [1, -8, 31], [1, 2, 37], [1, 4, 41], [1, 4, 43], [1, 2, 47], [1, 6, 53], [1, 0, 59], [1, -14, 61], [1, 2, 67], [1, -4, 71], [1, 10, 73], [1, -10, 79], [1, 12, 83], [1, -6, 89], [1, 10, 97]], 'index': 33, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11550/g'], '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': '2-11550-1.1-c1-0-33', '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': '2-11550-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.603500108532247, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1124966900825041005, 'z1': {'__RealLiteral__': 0, 'data': '1.037792526351240', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1124966900825041005', 'Lhash_array': ['1124966900825041005'], 'label': '2-11550-1.1-c1-0-33', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11550/g'}