-
lfunc_lfunctions • Show schema
Hide schema
{'A10': -2, 'A2': -1, 'A3': 1, 'A4': -1, 'A5': 2, 'A6': -1, 'A7': 0, 'A8': 3, 'A9': 1, 'Lhash': '1807661388308682976', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 142.02991007525148, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, -1]], [7, [1]], [11, [1]]], 'bad_primes': [3, 7, 11], 'central_character': '17787.1', 'coefficient_field': '1.1.1.1', 'conductor': 17787, 'conductor_radical': 231, 'degree': 2, 'euler_factors': [[1, 1, 2], [1, -1], [1, -2, 5], [1], [1], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 2, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-17787-1.1-c1-0-12', 'leading_term': '2.0440128021', '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/17787/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.044012802102822, 1.738139977766764, 0.8928497490287981, -0.1917558588675844, -0.9470976392394076, -0.8201233579098718, 0.2209588462488718, 1.438004892859637, 1.759771650352922, 0.7500047219599686, -0.7372257506120288, -1.073922729827029, 0.5985954199948814, 3.194023448441796, 4.327073812853072, 2.568344493678712, -0.8580341047891531, -3.012523928736443, -2.25188396958126, -0.1468510628527591, 0.1465595429928729, -2.397918248494268, -5.152188271949333, -4.669954188913068, -0.855286289759351, 2.613939325557675, 2.45246411270177, -0.4008305721429973, -2.083031441130823, -0.6417979189230083, 1.777882185599442, 2.088278408966243, 0.3231216592897291, -0.8603562170594264, -0.1603236194597845, 0.81438877275506, 0.4212656005786275, -0.4479957029138998, -0.1302020068464201, 0.8157048281773491, 0.618202532454033, -0.1944276106661794, 0.892038699921137, 3.787943799730771, 4.444742032468709, 0.4422532113084111, -4.176167225512351, -3.259718174205639, 2.843161892560024, 7.059223548868896, 4.917702871971187, 0.1622910583409105, -1.362312398165449, 0.1310548846635751, 0.3943330884384442, -1.075312802457218, -0.7399905941115581, 1.887848865362528, 2.727385905433812, 0.3707261070945205, -0.6316542714152513, 2.848746222174602, 6.468621089982342, 4.647432577162119, -0.4509589629863241, -2.055596331823572, 0.9046342426954175, 3.015384010268995, 1.542223579352647, -0.1900288897277744, 0.3052095440855799, 0.7525483206667948, -0.5062508077815417, -0.9771682605930634, 0.8816132999114703, 2.170241354741051, 0.8409114318204324, -0.4077140774604356, 0.4275084055723302, 0.3440731337765447, -2.723910570982174, -4.739206063240872, -2.183585453427112, 0.9944761043001689, -0.159873705749719, -2.797785063615709, -1.725468467056561, 0.6734092905027788, -0.8970673538709766, -3.770074959499183, -1.572064535545731, 3.31439804412489, 3.114732306453299, -0.9037717989489564, 0.1662049317756819, 6.819833988471259, 9.348347755074604, 4.044383563013706, -1.261138491679455, -0.9955645192429974, 0.6260887267086906, -0.2962202290960603, -0.8078070743935915, 1.049496384844345, 1.850790341393475, 0.1925503556384256, -0.5439565791933387, 0.4444193061268557, 0.0895746822429797, -1.134042495997051, 0.2347361687879595, 2.469642463964626, 0.8920890742720952, -2.53107954424822, -2.216403561432069, 0.3882495174675977, 0.2151205557466839, -0.6799473522275828, 2.20541248945616, 4.805367647288905, 1.164980179086224], 'positive_zeros': ['0.7045650789747930', '1.456967865338094', '2.369737489874612', '2.935579789055321', '3.937325413026200', '4.773410203600274', '5.025371784402288', '6.049327383188480', '6.716525565339301', '7.311030202032632', '8.043417754758536', '8.531873237522727', '9.103289507782321', '9.532907469406108', '10.16201132830474', '10.37428056260053', '11.27012166972771', '11.89356906246398', '12.76106503611736', '13.22885172798431', '13.57461274353071', '14.07973935457637', '14.78642022042977', '15.07498365087478', '15.97485726452203', '16.43744604165223', '17.19590693009921', '17.42512249283960', '17.91721799060089', '18.40277972035242', '19.11903700009088', '19.41041237543345', '19.79174186885333'], 'prelabel': '2-17787-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.917630220612295, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1807661388308682976, 'z1': {'__RealLiteral__': 0, 'data': '0.7045650789747930', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.456967865338094', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.369737489874612', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 142.02991007525148, 'bad_primes': [3, 7, 11], 'central_character': '1.1', 'conductor': 17787, 'conductor_radical': 231, 'degree': 2, 'dirichlet_coefficients': [1, -1, 1, -1, 2, -1, 0, 3, 1, -2, 0, -1, -2, 0, 2, -1, -2, -1, 0, -2, 0, 0, 8, 3, -1, 2, 1, 0, 6, -2, 8, -5, 0, 2, 0, -1, 6, 0, -2, 6, -2, 0, 0, 0, 2, -8, -8, -1, 0, 1, -2, 2, 6, -1, 0, 0, 0, -6, 4, -2, 6, -8, 0, 7, -4, 0, -4, 2, 8, 0, 0, 3, -14, -6, -1, 0, 0, 2, 4, -2, 1, 2, 12, 0, -4, 0, 6, 0, 6, -2, 0, -8, 8, 8, 0, -5, -2, 0, 0, 1], 'euler11': [1, 0, 0], 'euler13': [1, 2, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 2], 'euler23': [1, -8, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 0, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -6, 53], 'euler59': [1, -4, 59], 'euler61': [1, -6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, 0, 71], 'euler73': [1, 14, 73], 'euler79': [1, -4, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 2], [1, -1, 0], [1, -2, 5], [1, 0, 0], [1, 0, 0], [1, 2, 13], [1, 2, 17], [1, 0, 19], [1, -8, 23], [1, -6, 29], [1, -8, 31], [1, -6, 37], [1, 2, 41], [1, 0, 43], [1, 8, 47], [1, -6, 53], [1, -4, 59], [1, -6, 61], [1, 4, 67], [1, 0, 71], [1, 14, 73], [1, -4, 79], [1, -12, 83], [1, -6, 89], [1, 2, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/17787/o'], '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': '2-17787-1.1-c1-0-12', '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': '2-17787-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 11.917630220612295, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1807661388308682976, 'z1': {'__RealLiteral__': 0, 'data': '0.7045650789747930', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1807661388308682976', 'Lhash_array': ['1807661388308682976'], 'label': '2-17787-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/17787/o'}