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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': -1, 'A8': 0, 'A9': 1, 'Lhash': '1052640923995631127', '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': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 147.5635429353262, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '18480.1', 'coefficient_field': '1.1.1.1', 'conductor': 18480, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, 4, 59], [1, -6, 61], [1, 12, 67], [1, 0, 71], [1, -10, 73], [1, 8, 79], [1, -4, 83], [1, -10, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-18480-1.1-c1-0-7', 'leading_term': '1.56916093703', '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/18480/bg', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.569160937030027, 1.220526569669567, 0.2654251307282868, -0.934500898182736, -1.709117709944888, -1.408112330951872, 0.01378442531690327, 1.687705682908725, 2.293465683174546, 1.160240838376461, -0.90448041220351, -2.039818523497051, -0.9578218775892177, 1.642856552345145, 3.466481658528531, 2.774613026321624, 0.2427698798713883, -1.608992001598852, -1.073023900016307, 0.8590035642673765, 1.666880543080754, 0.3182961506354765, -1.497014774341087, -1.56053449510322, -0.02938769022863093, 0.8217477225206449, -0.1578183129412525, -1.191052816330409, -0.01754746263077801, 2.535517332519369, 3.115651944517478, 0.3942793271690434, -2.557032464056354, -1.920121974355559, 1.700484472198726, 3.844485193875191, 2.10042190302519, -0.7756863025982706, -0.9594490425170225, 1.083801934289664, 1.796572675405886, 0.2404094346630582, -0.591196546385206, 1.127892875513161, 2.766349197589761, 1.27047114453567, -1.787005080570916, -2.451863692687422, -0.5640251786986593, 0.163594554295449, -1.596376464005252, -2.595622630044303, -0.7527450849581958, 0.8469036710241551, -1.057953174863728, -3.985803480054987, -3.296127892089633, 0.08837744765453776, 0.8912554643995944, -1.84135465054697, -3.054129519768237, -0.1458326561765872, 2.542932261728674, 0.8983325586422978, -2.252452936634454, -2.143413504714581, 0.1407677097675306, 0.3875098493462021, -1.087299639396752, -0.7424862894354913, 0.9590879777771489, 0.3665193486677071, -1.910665471183612, -1.41294306340212, 1.8589342476855, 2.811635940887887, 0.3724264951489826, -0.3242060544931709, 2.566186376308352, 3.727062829267854, 0.3212925787624926, -2.166452456252831, 0.7837165371354026, 4.639285999654174, 3.610409292640375, 0.2524159610467287, -0.08327527538950653, 1.215096168133211, 0.02105991102409533, -1.930099836233842, -0.8398449708278019, 1.077245807591968, -0.1978111763623593, -2.300178809116981, -1.086512369310039, 0.7968856283858292, -1.070849568314851, -3.657204262046834, -1.778589655890116, 1.747877783194426, 1.212398173121297, -1.243874062190814, -0.4311271304327532, 1.100347171211819, -1.801019867214697, -5.700267320041708, -4.157009887494782, 0.1061029898928272, 0.3266040583846959, -1.80048211077805, -0.5236385797906683, 2.158079774245811, 0.8971753960743635, -2.040509634459048, -1.564511706169046, 0.1966106932937941, -0.8115228208399144, -1.887941068242287, 0.08976987647992568, 1.539239601893812, 0.1892676098494272], 'positive_zeros': ['0.5556143593437719', '1.498041251248678', '2.390941107076949', '3.098956202469107', '4.023295407016638', '4.640211357060898', '5.288734413746491', '6.004618238929894', '6.473232792414776', '7.001879702991683', '7.777189631945291', '8.390177542155349', '9.168288296743176', '9.624983068444776', '10.28452996465196', '10.62165595148809', '11.34955109915970', '12.08673331695323', '12.29079950836961', '13.07783274474702', '13.41060809188060', '14.24246853150291', '14.60071680849628', '15.25943453517136', '15.81377444878745', '16.48103004679724', '16.81840886651515', '17.35121632975541', '17.79073647562480', '18.36311352119613', '19.03989621653615', '19.29275624036059'], 'prelabel': '2-18480-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.147573541054452, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1052640923995631127, 'z1': {'__RealLiteral__': 0, 'data': '0.5556143593437719', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.498041251248678', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.390941107076949', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 147.5635429353262, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 18480, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -2, 0, -1, 0, 2, 0, -4, 0, 1, 0, 0, 0, 1, 0, -1, 0, 6, 0, 0, 0, -1, 0, -1, 0, 6, 0, 2, 0, -6, 0, 4, 0, 1, 0, 0, 0, 1, 0, -2, 0, -2, 0, 1, 0, 4, 0, -4, 0, 6, 0, -1, 0, -2, 0, -12, 0, 0, 0, 0, 0, 10, 0, -1, 0, -1, 0, -8, 0, 1, 0, 4, 0, 2, 0, -6, 0, 10, 0, 2, 0, 0, 0, -4, 0, 10, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 12, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, -10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, 0, 31], [1, -6, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, 2, 53], [1, 4, 59], [1, -6, 61], [1, 12, 67], [1, 0, 71], [1, -10, 73], [1, 8, 79], [1, -4, 83], [1, -10, 89], [1, -10, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/18480/bg'], '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': '2-18480-1.1-c1-0-7', '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': '2-18480-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.147573541054452, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1052640923995631127, 'z1': {'__RealLiteral__': 0, 'data': '0.5556143593437719', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1052640923995631127', 'Lhash_array': ['1052640923995631127'], 'label': '2-18480-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/18480/bg'}