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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': 2, 'A8': 0, 'A9': 1, 'Lhash': '323034880805983001', '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': [0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 92.75422698791934, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '11616.1', 'coefficient_field': '1.1.1.1', 'conductor': 11616, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 4, 5], [1, -2, 7], [1], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, -6, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, 8, 43], [1, -10, 47], [1, 12, 53], [1, 0, 59], [1, 8, 61], [1, -4, 67], [1, -6, 71], [1, 10, 73], [1, -6, 79], [1, -12, 83], [1, 14, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-11616-1.1-c1-0-1', 'leading_term': '1.40083041613', '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/11616/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.400830416128031, 1.067214413824719, 0.1146348320623637, -1.210961363752788, -2.351007844969284, -2.598055696571844, -1.556954520577026, 0.4166330725589382, 2.243033897870427, 2.782312120238684, 1.741912581130121, 0.04579000766316303, -0.8318696135965837, -0.1526985972246977, 1.346976631356114, 2.121409953950944, 1.395058788495567, 0.04235840451717359, -0.3627611298396541, 0.4824581790837955, 0.8455137468527232, -1.353638989554682, -5.911354654968988, -9.788380216834417, -9.764008862629638, -5.765275943070133, -1.13960200098303, 0.7015246728669629, -0.3735732301661739, -1.668066884522542, -1.197377362132904, 0.1427310258273298, 0.3749437831434215, -0.4953848547881987, -0.5607576777122449, 0.8114878004415492, 1.429843059075242, -0.866484445866123, -4.590632207836786, -5.687307343648076, -2.604077869542325, 1.360007155849647, 2.03874497058213, -0.3651334549633792, -1.940962506860309, -0.6669455848513867, 1.04800953197704, 0.3960783881401912, -1.461689095457701, -1.418254263803216, 0.3122591042456971, 0.138164392862415, -3.190755309275142, -5.885431918458887, -4.179418973885618, 0.07695589662596809, 1.848577639928094, -0.09326966988215812, -2.051200530895433, -1.401333860179474, -0.01409906539789085, -0.1285875085210379, -0.2742850300569622, 1.603452647185608, 3.44824916330012, 1.766650942816792, -2.048959069331715, -2.869125602176566, 0.1737504156044484, 1.726600270043433, -1.569050444361232, -5.382666673233142, -4.029238219057863, 0.8836151539188949, 3.11573961577721, 1.139854631128589, -0.7730158061415376, -0.2856950168992542, 0.1082067900916115, -1.067420970186689, -1.310712185955153, 0.5427993247110658, 1.326724805108324, -0.6292829701974386, -1.480933277411355, 1.761578076362455, 5.096082211109501, 3.496913744122855, -0.3223346124834065, 0.09011860821534019, 4.244700175314918, 5.55998388603876, 2.25123144665538, -0.4927541666577382, 0.006487364708429273, 0.1753699514647532, -1.945492925748092, -2.818813762843361, -0.7446631090083351, 0.2470006193745888, -1.827995187058921, -2.201026994098615, 2.253159234221662, 6.361085783856877, 4.625878739631514, 0.162932117998195, -1.047864511750363, 0.3420566642871173, 0.3841503598499543, -0.2680006108027058, 0.5956273938307406, 0.4545511653981677, -3.049534672398936, -5.413876837689991, -2.247532672112891, 1.399532947379236, -1.604825004296503, -7.652397621501382, -7.564163951411824, -1.599306152120713, 1.826802825033155], 'positive_zeros': ['0.5234190105425316', '1.700894543846752', '2.757628261145636', '3.277799823668986', '4.259838044433443', '4.632339921460955', '5.139201143139340', '6.596765531955217', '6.943777513611653', '7.717682173615206', '8.117661968180472', '8.619798145924143', '9.185362584436592', '10.15046442800272', '10.71664079855800', '11.32771709844640', '11.80170427199273', '12.45061908497672', '12.76619827493770', '13.74488951955920', '14.24141743033499', '15.00498698521983', '15.19659908270633', '15.56190364842451', '16.36305162383938', '16.98730257209895', '17.41277388706945', '18.20342626059342', '18.86233844258332', '19.32703484742406', '19.53863193850320'], 'prelabel': '2-11616-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.630899593907069, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 323034880805983001, 'z1': {'__RealLiteral__': 0, 'data': '0.5234190105425316', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.700894543846752', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.757628261145636', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.75422698791934, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 11616, 'conductor_radical': 66, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -4, 0, 2, 0, 1, 0, 0, 0, -4, 0, -4, 0, -2, 0, -4, 0, 2, 0, 6, 0, 11, 0, 1, 0, 6, 0, 4, 0, 0, 0, -8, 0, -2, 0, -4, 0, -6, 0, -8, 0, -4, 0, 10, 0, -3, 0, -2, 0, -12, 0, 0, 0, -4, 0, 0, 0, -8, 0, 2, 0, 16, 0, 4, 0, 6, 0, 6, 0, -10, 0, 11, 0, 0, 0, 6, 0, 1, 0, 12, 0, 8, 0, 6, 0, -14, 0, -8, 0, 4, 0, 16, 0, -18, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, -6, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -10, 47], 'euler5': [1, 4, 5], 'euler53': [1, 12, 53], 'euler59': [1, 0, 59], 'euler61': [1, 8, 61], 'euler67': [1, -4, 67], 'euler7': [1, -2, 7], 'euler71': [1, -6, 71], 'euler73': [1, 10, 73], 'euler79': [1, -6, 79], 'euler83': [1, -12, 83], 'euler89': [1, 14, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 4, 5], [1, -2, 7], [1, 0, 0], [1, 4, 13], [1, 2, 17], [1, 4, 19], [1, -6, 23], [1, -6, 29], [1, -4, 31], [1, 2, 37], [1, 6, 41], [1, 8, 43], [1, -10, 47], [1, 12, 53], [1, 0, 59], [1, 8, 61], [1, -4, 67], [1, -6, 71], [1, 10, 73], [1, -6, 79], [1, -12, 83], [1, 14, 89], [1, 18, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11616/q'], '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': '2-11616-1.1-c1-0-1', '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': '2-11616-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.630899593907069, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 323034880805983001, 'z1': {'__RealLiteral__': 0, 'data': '0.5234190105425316', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '323034880805983001', 'Lhash_array': ['323034880805983001'], 'factors': ['2-11616-1.1-c1-0-1'], 'label': '2-11616-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11616/q'}