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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 0, 'Lhash': '1698309943509457814', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 381.74880198333744, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [83, [1, -1]]], 'bad_primes': [2, 3, 83], 'central_character': '47808.1', 'coefficient_field': '1.1.1.1', 'conductor': 47808, 'conductor_radical': 498, 'degree': 2, 'euler_factors': [[1], [1], [1, 2, 5], [1, 4, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 4, 19], [1, 2, 23], [1, 0, 29], [1, -4, 31], [1, 2, 37], [1, -2, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -12, 71], [1, -2, 73], [1, -10, 79], [1, -1], [1, -2, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 20, 'label': '2-47808-1.1-c1-0-20', 'leading_term': '3.33097514178', '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/47808/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7056844132290231, 0.6851206837048764, -0.4989927215067764, -2.50094367119496, -4.036589928118797, -3.690452658504252, -1.30788390034386, 1.428559338366492, 2.265299025778745, 0.6022173957805255, -1.712407683726088, -2.275720284084481, -0.8340719123209619, 0.50812009823258, 0.1105980273808553, -0.9062263183556722, -0.2473151027503416, 1.89784023473979, 2.394885891238767, -0.7070706424132612, -4.86154003287938, -5.699603803995917, -2.645238238753021, 0.3904366497733336, 0.4976833934555946, -0.4962741270690234, 0.3881176874846905, 2.086576357397155, 1.169508684722901, -2.097388676029648, -3.415867891287437, -1.023727125096435, 1.39377647552011, 0.6164366844722383, -0.9563311920489203, 0.2833727656645137, 2.565449302812775, 1.599155628826366, -1.683128178180373, -2.182189861278092, 0.7552003024060864, 2.135233084990969, -0.01920082851990296, -1.338088311409562, 0.8562696407893358, 2.629047355556092, 0.6902631709513835, -1.464410773534167, 0.001215244099675475, 2.169146618536077, 0.9497562631065636, -1.299463297842379, -0.7623699211197703, 0.05959222470555647, -2.423728225039175, -4.386766086174652, -0.459255901275889, 5.634239257346262, 6.098378774176376, 1.677179991151009, -0.7241671601665095, -0.06102027098000411, -0.4663031105111971, -1.566488911157093, -0.2103841165408326, 1.228359104407963, -0.8724079082846699, -2.517386925455646, 1.339893440700397, 5.939702567233762, 4.174716820323381, -0.384168634950961, -0.1470904871117771, 2.766376878045725, 1.913078719591513, -0.915247859197624, -0.6739476690126086, 0.6754903850490339, -0.00172151658890921, 0.4304417901893301, 3.227197499726289, 2.762440163533098, -1.829343744465428, -2.652828985357379, 2.114892827365467, 3.90736234962518, 0.03451246613630397, -1.73060078228621, 1.080741954325798, 2.032633334796271, -0.1251931721630965, -0.4432794961094062, 0.2002462560825792, -1.941814318561099, -3.239382174594308, -0.3412551756524296, 0.6677392248466614, -3.712596128548298, -5.789776566110964, -1.673342309448865, 0.8601201205687244, -1.658206106862554, -2.54804999338673, -0.3025328824453137, -0.5540389314864786, -2.023586057954641, 0.2842264382666475, 2.237343031750658, -1.060153256041509, -3.650881501291024, -0.963686215426913, 0.6553690318742972, -1.757781630584986, -2.062256443111926, -0.01543881634295471, -1.55829724311697, -3.843263614158717, -0.9761743547155154, 1.688091818343347, -1.410140663366012], 'positive_zeros': ['0.6710982969914153', '1.860158875968290', '2.560183061685185', '3.374246391642660', '3.774119796523465', '4.283058840266103', '4.958633234047375', '5.951082913739422', '6.353654762861307', '6.693293256397119', '7.345445145299373', '8.080757388701969', '8.576004377729814', '8.971202459249564', '9.619909509825796', '10.19157234210520', '10.74821314854606', '11.17717276758411', '11.80731919279491', '12.24989067640723', '12.83767552035564', '13.38638192952116', '13.51677017820208', '14.26756151421920', '15.11844296510510', '15.52607625390770', '15.63345887360288', '16.27279951416457', '16.67880619155033', '17.18995340093967', '17.96989899199131', '18.26264426816338', '18.90245488129004', '19.34604978503854', '19.74954305255151', '19.93733655923828'], 'prelabel': '2-47808-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.53839302458975, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1698309943509457814, 'z1': {'__RealLiteral__': 0, 'data': '0.6710982969914153', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.860158875968290', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.560183061685185', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 381.74880198333744, 'bad_primes': [2, 3, 83], 'central_character': '1.1', 'conductor': 47808, 'conductor_radical': 498, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, -4, 0, 0, 0, 0, 0, 4, 0, 0, 0, -6, 0, -4, 0, 0, 0, -2, 0, -1, 0, 0, 0, 0, 0, 4, 0, 0, 0, 8, 0, -2, 0, 0, 0, 2, 0, -8, 0, 0, 0, 0, 0, 9, 0, 0, 0, 6, 0, 0, 0, 0, 0, 4, 0, -10, 0, 0, 0, -8, 0, -4, 0, 0, 0, 12, 0, 2, 0, 0, 0, 0, 0, 10, 0, 0, 0, 1, 0, 12, 0, 0, 0, 2, 0, -16, 0, 0, 0, 8, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 2, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 0, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, 10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -2, 73], 'euler79': [1, -10, 79], 'euler83': [1, -1, 0], 'euler89': [1, -2, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 2, 5], [1, 4, 7], [1, 0, 11], [1, -4, 13], [1, 6, 17], [1, 4, 19], [1, 2, 23], [1, 0, 29], [1, -4, 31], [1, 2, 37], [1, -2, 41], [1, 8, 43], [1, 0, 47], [1, -6, 53], [1, -4, 59], [1, 10, 61], [1, 4, 67], [1, -12, 71], [1, -2, 73], [1, -10, 79], [1, -1, 0], [1, -2, 89], [1, -6, 97]], 'index': 20, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/47808/k'], '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': '2-47808-1.1-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': 1, 'prelabel': '2-47808-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.53839302458975, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1698309943509457814, 'z1': {'__RealLiteral__': 0, 'data': '0.6710982969914153', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1698309943509457814', 'Lhash_array': ['1698309943509457814'], 'factors': ['2-47808-1.1-c1-0-20'], 'label': '2-47808-1.1-c1-0-20', 'type': 'ECQ', 'url': 'EllipticCurve/Q/47808/k'}