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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '571716533230188721', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 101.37807040621763, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '12696.1', 'coefficient_field': '1.1.1.1', 'conductor': 12696, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 2, 5], [1, -1, 7], [1, 2, 11], [1, -1, 13], [1, -2, 17], [1, 0, 19], [1], [1, 2, 29], [1, 0, 31], [1, -1, 37], [1, 0, 41], [1, -1, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, -1, 61], [1, 5, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, -6, 83], [1, -8, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-12696-1.1-c1-0-13', 'leading_term': '3.36365432775', '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/12696/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7861251626528099, 1.230548724236315, 0.9975525435701528, -0.02964649957769772, -1.469232889439689, -2.444848863876949, -2.071772735079036, -0.2002167389689288, 2.192866772663747, 3.492552653095624, 2.664021285015996, 0.2483054974833839, -1.895642075043349, -2.131327425119239, -0.5655986738615828, 1.009210795186241, 0.9012857269931699, -0.6921374882156914, -1.87687306826693, -1.207187486552414, 0.5506636227625727, 1.208771509684243, -0.1967826495874599, -2.021615386036582, -1.804706056917971, 0.6902565679230439, 2.965270855142972, 2.716778624072403, 0.6813282337654493, -0.3434575497055845, 0.776290504320109, 1.961310284318251, 0.8664923823332674, -1.499597597127345, -1.68211090608999, 1.526133031502609, 4.911330925593971, 4.598913890091629, 1.059946303871839, -1.45462430053472, -0.4531392486436555, 1.826148107163787, 1.981928217393592, 0.2286362036702714, -0.490152280893442, 0.6712417703622306, 1.313476235839747, 0.02997650377903828, -0.960388901143024, 0.6087650253674781, 2.853226821035198, 2.189184897947994, -0.7644658597402907, -1.368803884259492, 2.129284397444537, 5.372361177940996, 3.912333501370378, -0.2657719342964569, -1.745933002179544, 0.3530608460898916, 1.719899047630025, 0.07325030461466027, -1.599673576688615, -0.6547473536625096, 0.6493349373237399, -0.5829702154192891, -2.387907527099019, -1.08438578127512, 2.133266870658299, 2.780849922314413, 0.5381169490614031, -0.2552282932078576, 1.870920264996973, 3.023273602642624, 0.9650527279351423, -0.7659508945037923, 0.7632745579198095, 2.230248959776041, -0.3234119066779177, -4.094204829712026, -3.757129685503385, -0.4670238482915792, 0.1844072133176254, -2.114165236769315, -2.124692958401554, 1.294584256096898, 2.912960632038563, 0.3360085809743152, -1.812865340212522, -0.08221912677172827, 2.141732863204993, 1.243405668507939, -0.5073667994776311, -0.2285884120527958, -0.04695863561994036, -2.013321200462949, -2.912519900506188, -0.3606615828299152, 1.174252826201873, -2.414791216848408, -6.494389669619493, -4.659795856909192, 0.1151761848328144, 0.3535701110931253, -3.227416047022925, -3.699216707259827, -0.345548828126282, 1.093365954753068, -0.5828326698431263, -0.9560661905903641, 0.5295502570006019, -0.03762617197525655, -2.247074196824859, -1.778463742956758, 0.4507494464282742, -0.558265615947766, -3.748238259820727, -3.274648698006151, 0.2858655669134714, 0.6919599420870021], 'positive_zeros': ['0.9944734700913198', '2.020823765864921', '3.023711053660488', '3.824277992594454', '4.402911119017581', '5.169827542517263', '5.725844157769832', '6.440773120963800', '7.352148113091306', '7.621087823946684', '8.339154763367204', '8.902609561274123', '9.824869239328240', '10.29683587809196', '11.03566743007182', '11.38183581499391', '12.00438460017363', '12.43702749440930', '13.18313135849600', '13.62297153118489', '14.48194442781752', '14.96604888798346', '15.50763118560653', '16.09124013161308', '16.42994405447312', '17.08319790971857', '17.81813903269210', '18.04853554882902', '18.84437166104109', '19.16857350388615', '19.73041274263071'], 'prelabel': '2-12696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.068667757266482, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 571716533230188721, 'z1': {'__RealLiteral__': 0, 'data': '0.9944734700913198', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.020823765864921', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.023711053660488', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 101.37807040621763, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 12696, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -2, 0, 1, 0, 1, 0, -2, 0, 1, 0, 2, 0, 2, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, -2, 0, 0, 0, 2, 0, -2, 0, 1, 0, -1, 0, 0, 0, 1, 0, -2, 0, 4, 0, -6, 0, -2, 0, 6, 0, 4, 0, 0, 0, 8, 0, 1, 0, 1, 0, -2, 0, -5, 0, 0, 0, -8, 0, -6, 0, 1, 0, -2, 0, 0, 0, 1, 0, 6, 0, -4, 0, 2, 0, 8, 0, 1, 0, 0, 0, 0, 0, -10, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, -1, 13], 'euler17': [1, -2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -1, 37], 'euler41': [1, 0, 41], 'euler43': [1, -1, 43], 'euler47': [1, -4, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -8, 59], 'euler61': [1, -1, 61], 'euler67': [1, 5, 67], 'euler7': [1, -1, 7], 'euler71': [1, 8, 71], 'euler73': [1, 6, 73], 'euler79': [1, 0, 79], 'euler83': [1, -6, 83], 'euler89': [1, -8, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 2, 5], [1, -1, 7], [1, 2, 11], [1, -1, 13], [1, -2, 17], [1, 0, 19], [1, 0, 0], [1, 2, 29], [1, 0, 31], [1, -1, 37], [1, 0, 41], [1, -1, 43], [1, -4, 47], [1, -6, 53], [1, -8, 59], [1, -1, 61], [1, 5, 67], [1, 8, 71], [1, 6, 73], [1, 0, 79], [1, -6, 83], [1, -8, 89], [1, 10, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/12696/f'], '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': '2-12696-1.1-c1-0-13', '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': '2-12696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.068667757266482, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 571716533230188721, 'z1': {'__RealLiteral__': 0, 'data': '0.9944734700913198', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '571716533230188721', 'Lhash_array': ['571716533230188721'], 'label': '2-12696-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/12696/f'}