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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': 1, 'Lhash': '530165502983979587', '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': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 211.76326616043568, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [13, [1, -1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '26520.1', 'coefficient_field': '1.1.1.1', 'conductor': 26520, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 0, 7], [1, -4, 11], [1, -1], [1, -1], [1, 8, 19], [1, 8, 23], [1, -6, 29], [1, 0, 31], [1, 6, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, 10, 53], [1, 0, 59], [1, -6, 61], [1, 0, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, -14, 97]], 'gamma_factors': [[], [0]], 'index': 3, 'label': '2-26520-1.1-c1-0-3', 'leading_term': '2.41560627248', '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/26520/x', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.415606272483656, 1.930273277569967, 0.5951064420446648, -1.113159602651949, -2.3322169807643, -2.268755918684225, -0.9261035089304973, 0.6285138931084092, 0.9861782070956123, -0.301049297469737, -2.086802773583862, -2.568507695375416, -1.120589965913121, 0.9082792219358915, 1.570172277130814, 0.5487930305992688, -0.4272232571620625, 0.1914058196817743, 1.471657970375541, 0.8045281298625307, -2.654915617170398, -6.191221219135029, -6.235633812248385, -2.70207757062207, 0.6585763414592172, 0.7942787005469168, -0.9335676773168357, -0.8986815205191253, 1.607401195419576, 3.397096385054591, 2.047589599300772, -0.5663090366980059, -1.102096451700506, 0.3368003037323318, 0.7413357248259321, -0.7124406542364771, -1.25889074350341, 0.6837010251483339, 2.338140170837437, 0.7235759635832202, -2.180610611537215, -2.08232445985531, 0.7361494752960391, 1.510170645452645, -1.439225288787484, -3.743405596632381, -1.836001082045379, 1.335746849422068, 1.215298158662506, -0.9605005965537854, -0.7205661277319825, 1.57719632702445, 1.232628288569185, -2.431828370942557, -4.42229914711661, -2.220889763866684, 0.3698676663627823, 0.1633463669500799, -0.3192126689535943, 1.509342556542315, 2.894126238424232, 0.9649984254761864, -1.291805157541768, -0.1870857240642425, 1.600754836154915, -0.1505430057358853, -2.824677588722918, -1.16326793605307, 2.857456664351708, 3.027126572464523, 0.08339745094081188, 0.4485898004416185, 4.306339808357388, 4.904468306799531, 0.5827847206041046, -2.445761959652912, -1.116798083452742, 0.3758862612205652, -0.2629666046909241, 0.1857681650524191, 2.332964133146294, 2.079801913491415, -0.6569049781173759, -0.7850132209872513, 1.954886757965783, 1.9329657259653, -1.270339521774822, -1.619076965456441, 1.4398876496705, 1.540437395316632, -1.929589943504012, -2.178736084818459, 1.679445153113803, 2.618543914528034, -0.7616071109530196, -1.948987857335275, 0.3121701210983133, 0.09408544357792203, -3.039290823603311, -3.0423202220789, 0.2077815448025244, 0.9184038682268486, -0.7252172935989417, 0.129551103371675, 1.934216831028979, 0.09608715807971505, -2.37739729003761, -0.413773883244743, 2.470723010865219, 1.188425548578857, -0.8509555690098204, 0.1108988566736402, 0.01628041589779498, -2.698385936326038, -1.161379170266395, 5.931076848302696, 8.762472203292702, 3.404700322726554, -1.233026307322799, -0.1350709357800402, 0.8372205430707537], 'positive_zeros': ['0.5877237924917512', '1.637490171263562', '2.207796173120936', '3.130014156678169', '3.856249345758655', '4.212167255953597', '4.824932986731635', '5.931715308778547', '6.365227930673726', '6.856692652060138', '7.686662946745351', '8.194715073928983', '8.643507865577362', '9.181474761271823', '9.807342700282696', '10.43545510093207', '10.89963117390699', '11.62835071711745', '12.13274870972643', '12.58001857485359', '13.09649399337437', '13.94273451426500', '14.28753101783345', '14.57275109340675', '15.33162297916699', '15.76934018696402', '16.23833432261299', '16.81907831648016', '17.50986080300622', '17.70642707489248', '18.53069543967615', '19.13831191734178', '19.42495861550960', '19.72191296345175'], 'prelabel': '2-26520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.552088034383097, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 530165502983979587, 'z1': {'__RealLiteral__': 0, 'data': '0.5877237924917512', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.637490171263562', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.207796173120936', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 211.76326616043568, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 26520, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 4, 0, 1, 0, -1, 0, 1, 0, -8, 0, 0, 0, -8, 0, 1, 0, 1, 0, 6, 0, 0, 0, 4, 0, 0, 0, -6, 0, 1, 0, 6, 0, 4, 0, -1, 0, 4, 0, -7, 0, 1, 0, -10, 0, -4, 0, -8, 0, 0, 0, 6, 0, 0, 0, -1, 0, 0, 0, -8, 0, 0, 0, -2, 0, 1, 0, 0, 0, 8, 0, 1, 0, 0, 0, -1, 0, 6, 0, 2, 0, 0, 0, 0, 0, 8, 0, 14, 0, 4, 0], 'euler11': [1, -4, 11], 'euler13': [1, -1, 0], 'euler17': [1, -1, 0], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 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, -4, 47], 'euler5': [1, 1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 0, 59], 'euler61': [1, -6, 61], 'euler67': [1, 0, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, -2, 89], 'euler97': [1, -14, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 0, 7], [1, -4, 11], [1, -1, 0], [1, -1, 0], [1, 8, 19], [1, 8, 23], [1, -6, 29], [1, 0, 31], [1, 6, 37], [1, -6, 41], [1, -4, 43], [1, -4, 47], [1, 10, 53], [1, 0, 59], [1, -6, 61], [1, 0, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, 0, 83], [1, -2, 89], [1, -14, 97]], 'index': 3, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/26520/x'], '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': '2-26520-1.1-c1-0-3', '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': '2-26520-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.552088034383097, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 530165502983979587, 'z1': {'__RealLiteral__': 0, 'data': '0.5877237924917512', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '530165502983979587', 'Lhash_array': ['530165502983979587'], 'label': '2-26520-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/26520/x'}