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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': -1, 'A8': 1, 'A9': 1, 'Lhash': '1719208501744957812', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 146.5574278698581, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [7, [1, 1]], [19, [1, 1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '18354.1', 'coefficient_field': '1.1.1.1', 'conductor': 18354, 'conductor_radical': 18354, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1, 0, 5], [1, 1], [1, -4, 11], [1, 3, 13], [1, 5, 17], [1, 1], [1, 1], [1, 10, 29], [1, -4, 31], [1, 8, 37], [1, 1, 41], [1, 1, 43], [1, -12, 47], [1, 1, 53], [1, 0, 59], [1, -13, 61], [1, 4, 67], [1, -9, 71], [1, 1, 73], [1, -7, 79], [1, -4, 83], [1, 4, 89], [1, -1, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-18354-1.1-c1-0-1', 'leading_term': '1.99903721802', '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/18354/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.999037218023615, 1.522263143909098, 0.1766838689696938, -1.654145171502292, -3.179550323058936, -3.516302566705584, -2.360475256955073, -0.4556666871596672, 0.7350581001970857, 0.1410135327147437, -1.875314010733691, -3.623919426116662, -3.510853474123482, -1.570546621345346, 0.4922152942107138, 0.9973873846768136, 0.03928342804702653, -0.6904168423380923, 0.05864996210243825, 1.537922065903085, 1.907472156162838, 0.6228173243716439, -0.7399025806335443, -0.4753580526887795, 0.9384048698013205, 1.439218932355796, 0.3164608778027295, -0.6222495128835096, 0.290921017688677, 1.602770267181326, 0.1808384686382681, -4.062256253420347, -6.745089003829104, -3.979252670154396, 2.157986476755518, 5.423064334290745, 2.999846413577983, -1.00936798224465, -1.176585789812459, 2.05413077379369, 3.485068864177226, 0.8027270659034773, -2.328881207540345, -1.909664247973629, 0.7356676750319442, 1.554025129570008, 0.0162486640605725, -0.7922718110302236, 0.281531492729181, 0.7622190252595715, -0.7231143331524115, -1.74075365051145, -0.2707856003840753, 1.461177656261964, 0.571593186695918, -1.352864056164723, -0.7274466111512017, 1.751989576991506, 1.953786012783402, -0.7105457309075094, -2.157226983886528, -0.6072798875680985, 0.4098128317416192, -1.48568218844709, -2.96178734454105, -0.760796306030799, 2.238254429746666, 1.815773690499901, -0.2568833609759236, 0.1612833591714395, 1.332787850508613, -1.510834926266098, -6.322377988906916, -5.734358804725682, 0.8123919071143677, 5.072026323716481, 2.688153166526426, -0.5627795312201945, 0.6491526983230032, 2.609410461852808, 0.5177316583522585, -2.289623877832249, -0.6573793343246144, 2.622370592238105, 1.66378720530321, -2.174683235750469, -3.13123306697204, -0.9458963063654442, 0.1590896536270232, -0.3376544005854019, 0.04955847074288451, 0.4427658468473065, -1.40724585607775, -3.243209457119818, -1.84706666502224, 0.3877673677327109, -0.245042308780437, -1.53229641257356, -0.05745401892851707, 1.424165377557412, -0.2314070254769663, -0.8093998849111135, 3.620282921885485, 7.268934115022639, 3.76464742402068, -1.445158098969877, 0.01398425254904886, 4.363476908946241, 2.853565848457327, -1.950494208217081, -1.469742708997582, 2.641101801098979, 2.365071085939479, -1.265191821470458, -1.196982966222843, 1.61911405996402, 1.111624096475767, -1.544216936402881, -1.265439192048987, 0.422614882605849, -0.1526526181184574], 'positive_zeros': ['0.5257746861502579', '1.817685042846408', '2.272404371254269', '3.427072022607755', '4.008428035164818', '4.489419770783477', '5.343863002901317', '5.839730935088926', '6.556012218232041', '6.953421390086885', '7.513505793987145', '8.412161967889895', '9.172810754237444', '9.602442186642584', '10.30236662548621', '10.92752531554042', '11.50237378890453', '11.94781456851894', '12.40173013577355', '13.02983074020449', '13.56549202738657', '14.07486132697441', '14.68961751433458', '15.33062882172518', '15.58913611673910', '16.30314934092488', '16.95590468409502', '17.22501706616034', '17.66384781589262', '18.47134722266607', '19.17716021961666', '19.43726087305180'], 'prelabel': '2-18354-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.106090527906112, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1719208501744957812, 'z1': {'__RealLiteral__': 0, 'data': '0.5257746861502579', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.817685042846408', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.272404371254269', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 146.5574278698581, 'bad_primes': [2, 3, 7, 19, 23], 'central_character': '1.1', 'conductor': 18354, 'conductor_radical': 18354, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, -1, 1, 1, 0, 4, -1, -3, -1, 0, 1, -5, 1, -1, 0, 1, 4, -1, -1, -5, -3, -1, -1, -10, 0, 4, 1, -4, -5, 0, 1, -8, -1, 3, 0, -1, 1, -1, 4, 0, -1, 12, -1, 1, -5, 5, -3, -1, -1, 0, -1, 1, -10, 0, 0, 13, 4, -1, 1, 0, -4, -4, -5, 1, 0, 9, 1, -1, -8, 5, -1, -4, 3, 7, 0, 1, -1, 4, 1, 0, -1, 10, 4, -4, 0, 3, -1, -4, 12, 0, -1, 1, 1, 4, -5], 'euler11': [1, -4, 11], 'euler13': [1, 3, 13], 'euler17': [1, 5, 17], 'euler19': [1, 1, 0], 'euler2': [1, -1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 10, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 8, 37], 'euler41': [1, 1, 41], 'euler43': [1, 1, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 5], 'euler53': [1, 1, 53], 'euler59': [1, 0, 59], 'euler61': [1, -13, 61], 'euler67': [1, 4, 67], 'euler7': [1, 1, 0], 'euler71': [1, -9, 71], 'euler73': [1, 1, 73], 'euler79': [1, -7, 79], 'euler83': [1, -4, 83], 'euler89': [1, 4, 89], 'euler97': [1, -1, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 5], [1, 1, 0], [1, -4, 11], [1, 3, 13], [1, 5, 17], [1, 1, 0], [1, 1, 0], [1, 10, 29], [1, -4, 31], [1, 8, 37], [1, 1, 41], [1, 1, 43], [1, -12, 47], [1, 1, 53], [1, 0, 59], [1, -13, 61], [1, 4, 67], [1, -9, 71], [1, 1, 73], [1, -7, 79], [1, -4, 83], [1, 4, 89], [1, -1, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/18354/r'], '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': '2-18354-1.1-c1-0-1', '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': '2-18354-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.106090527906112, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1719208501744957812, 'z1': {'__RealLiteral__': 0, 'data': '0.5257746861502579', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1719208501744957812', 'Lhash_array': ['1719208501744957812'], 'label': '2-18354-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/18354/r'}