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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 0, 'Lhash': '1413468727162649817', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 247.2168446578842, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [43, [1, 1]]], 'bad_primes': [2, 3, 5, 43], 'central_character': '30960.1', 'coefficient_field': '1.1.1.1', 'conductor': 30960, 'conductor_radical': 1290, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, 3, 7], [1, 0, 11], [1, -5, 13], [1, -4, 17], [1, -7, 19], [1, 4, 23], [1, 3, 29], [1, 3, 31], [1, 4, 37], [1, -11, 41], [1, 1], [1, 2, 47], [1, 10, 53], [1, 4, 59], [1, 11, 61], [1, 1, 67], [1, 14, 71], [1, 3, 73], [1, 13, 79], [1, 8, 83], [1, -4, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 43, 'label': '2-30960-1.1-c1-0-43', 'leading_term': '5.95755838353', '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/30960/be', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.394993534288684, 2.221967557462742, 2.01851663700742, 0.8156882024475154, -0.5628038630399033, -0.8790745383473928, 0.4830319789013829, 2.708076306214873, 3.987738559434986, 3.147042775904466, 0.9451051261172708, -0.547259298051691, -0.1746304456223273, 0.8788871698788739, 0.4134477850978273, -1.919975712437061, -3.716203164046164, -2.460887969850943, 1.185846410896345, 3.755149880341105, 2.9714425250136, 0.4249773685281007, -0.7235976695737698, -0.02606544345846017, -0.04086239469103262, -2.135079706333481, -3.995483048804629, -2.907109976882267, -0.1708663504111444, 0.3259832047543895, -2.129454407530683, -3.616538364021948, -1.193068984775797, 2.566536057765993, 3.200700446645181, 0.837878075304154, -0.4409763533220212, 0.8075024383094753, 1.546511718130768, 0.007362104008467326, -0.9259299718149198, 1.197907883428591, 3.478682153534834, 1.995541033988731, -1.32936967297006, -1.33240973321266, 1.953841808141226, 3.188641116940174, 0.4783611048819798, -1.729609497856157, -0.4397273296104571, 1.081047091738831, -0.3298034118872421, -2.017274402509063, -0.848850518310968, 0.5919485189975736, -0.9892567720734364, -2.503737618453839, 0.6453338830983584, 5.646748109510836, 5.955677865006397, 1.913983565229877, -0.3909186182422219, 0.3773364245695509, 0.1031976740221472, -1.497549262549885, -0.2498919570722231, 3.196606268155366, 3.032414753285212, -1.178355780568717, -3.104792615316703, -0.7796738291872418, 0.5462799257636907, -1.058920964790486, -0.9932363581300206, 1.79245126583496, 2.039572368172727, -1.225019801512088, -2.027425906432193, 1.219882958275961, 2.63539347295827, 0.3888293041323887, -0.09168864454578807, 2.423143432248452, 2.232513369094278, -1.5090272875048, -2.515044118561805, 0.4300623504432703, 1.400221851022432, -0.6943043939948323, -0.8133924411203174, 0.7974574242045614, -0.8010347449343834, -3.654911558963691, -1.732319588355477, 2.299036248496803, 1.240229027669752, -2.666132036672331, -2.1803205414847, 0.9279052046036713, 0.3797183862317372, -1.964408607775474, -1.234475365802905, 0.2475925574496154, -0.1912969641761253, 1.62637412032332, 6.601929443154643, 7.217694024969292, 1.562516916057104, -1.585023139647132, 1.212537443890018, 2.659062836506857, 0.1324298483714231, -0.4751876440923679, 1.369418301769121, 0.3725916391867087, -1.878850456946921, -0.3600886110868736, 1.664567531633562, -0.1952907772621333], 'positive_zeros': ['1.137364769803711', '1.686953212720659', '2.873196736981550', '3.288369884721706', '3.806357716412780', '4.673198554280015', '5.551335664782913', '6.007934037280167', '6.240725330754514', '7.270599911349055', '7.549001963917171', '8.323203055118812', '9.098681651617793', '9.375232338975099', '10.00094421853987', '10.39469783991609', '11.13971486227855', '11.61092235790150', '12.28569803842502', '12.79862004444034', '13.21443808824016', '13.85336074551572', '14.14474849738328', '14.71820539928510', '15.65563529716636', '15.91172271362706', '16.26637894401024', '16.76911259447791', '17.43361775023400', '18.07776306886443', '18.35911723186827', '18.84706628359053', '19.41141130459811', '19.91652935541595'], 'prelabel': '2-30960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.72313087962713, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1413468727162649817, 'z1': {'__RealLiteral__': 0, 'data': '1.137364769803711', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.686953212720659', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.873196736981550', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 247.2168446578842, 'bad_primes': [2, 3, 5, 43], 'central_character': '1.1', 'conductor': 30960, 'conductor_radical': 1290, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, -3, 0, 0, 0, 0, 0, 5, 0, 0, 0, 4, 0, 7, 0, 0, 0, -4, 0, 1, 0, 0, 0, -3, 0, -3, 0, 0, 0, -3, 0, -4, 0, 0, 0, 11, 0, -1, 0, 0, 0, -2, 0, 2, 0, 0, 0, -10, 0, 0, 0, 0, 0, -4, 0, -11, 0, 0, 0, 5, 0, -1, 0, 0, 0, -14, 0, -3, 0, 0, 0, 0, 0, -13, 0, 0, 0, -8, 0, 4, 0, 0, 0, 4, 0, -15, 0, 0, 0, 7, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -5, 13], 'euler17': [1, -4, 17], 'euler19': [1, -7, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, 4, 37], 'euler41': [1, -11, 41], 'euler43': [1, 1, 0], 'euler47': [1, 2, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 4, 59], 'euler61': [1, 11, 61], 'euler67': [1, 1, 67], 'euler7': [1, 3, 7], 'euler71': [1, 14, 71], 'euler73': [1, 3, 73], 'euler79': [1, 13, 79], 'euler83': [1, 8, 83], 'euler89': [1, -4, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 3, 7], [1, 0, 11], [1, -5, 13], [1, -4, 17], [1, -7, 19], [1, 4, 23], [1, 3, 29], [1, 3, 31], [1, 4, 37], [1, -11, 41], [1, 1, 0], [1, 2, 47], [1, 10, 53], [1, 4, 59], [1, 11, 61], [1, 1, 67], [1, 14, 71], [1, 3, 73], [1, 13, 79], [1, 8, 83], [1, -4, 89], [1, -6, 97]], 'index': 43, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/30960/be'], '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': '2-30960-1.1-c1-0-43', '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': '2-30960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.72313087962713, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1413468727162649817, 'z1': {'__RealLiteral__': 0, 'data': '1.137364769803711', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1413468727162649817', 'Lhash_array': ['1413468727162649817'], 'label': '2-30960-1.1-c1-0-43', 'type': 'ECQ', 'url': 'EllipticCurve/Q/30960/be'}