-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '2073482534485997374', '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': 202.75614081243526, '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': '25392.1', 'coefficient_field': '1.1.1.1', 'conductor': 25392, 'conductor_radical': 138, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1, 5], [1, 0, 7], [1, 0, 11], [1, 5, 13], [1, -2, 17], [1, 4, 19], [1], [1, 5, 29], [1, 4, 31], [1, 10, 37], [1, 5, 41], [1, 8, 43], [1, -4, 47], [1, -11, 53], [1, -4, 59], [1, 1, 61], [1, -4, 67], [1, -12, 71], [1, -3, 73], [1, -4, 79], [1, -16, 83], [1, 9, 89], [1, 5, 97]], 'gamma_factors': [[], [0]], 'index': 4, 'label': '2-25392-1.1-c1-0-4', 'leading_term': '1.22789303722', '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/25392/v', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.227893037218486, 0.7289863962830705, -0.6405326128664749, -2.389840097476447, -3.637425911318938, -3.555700479606453, -2.094652138177425, -0.2775375433488234, 0.4668043403360683, -0.421843381959309, -1.951861600659134, -2.409944898473367, -1.129160505566599, 0.6583888965421288, 1.082059688485615, -0.1504289853414881, -1.203108035158333, -0.2345478967333942, 2.134642253131258, 3.269328161522979, 1.809211648711973, -0.2098708377562419, 0.4421876120033557, 3.954039115356277, 6.711287431082627, 5.529458724577198, 1.694855284734301, -0.6337952497408118, 0.2634552910444191, 1.801316771549458, 1.159096972525839, -0.6776411285512386, -0.8115622306641477, 0.7625630588028243, 1.022223368727398, -1.170632590457927, -2.924923476217071, -1.733312830389979, 0.3782069619827107, -0.06784749376061154, -2.264974661340425, -2.22301721802323, 0.527385323119599, 1.559775052801386, -1.542608759677061, -4.855938806701809, -3.840945220114631, -0.3092844280667104, 0.693667032853084, -0.9799397929020864, -0.903225526911044, 1.901102565177029, 3.136913602724244, 0.8221254660404475, -0.9903109381999377, 0.9335811290571997, 3.466086709363513, 2.596450796353059, 0.1654959874024342, 0.02639049875113287, 1.050518546854602, -0.03649267852069245, -1.611262863859421, 0.1798613658755043, 3.472751233055523, 2.930230662832321, -0.7780900462205036, -1.75535563714973, 0.6179708834963086, 0.5956691001067302, -3.018743162353683, -3.959562550427039, 0.407049464210896, 3.976653677420765, 2.272053181119923, -0.4723104158174766, 0.2506948628154018, 1.712176418792753, 0.6265144342722107, -0.3619744585479677, 0.9901661416213166, 1.182194012082153, -1.787930013124818, -3.372808763926039, -0.9252091913673135, 0.7497657787710978, -1.368103684193037, -2.373654613271249, 0.7638448017261174, 2.60640568043741, -0.279849129616936, -2.076142095442551, 1.311865958778881, 4.14510701976529, 1.713177826992533, -1.060983498414027, 0.1804921270408734, 1.119941389014712, -1.460904482058212, -2.814369222551963, -0.3084721124182831, 0.9246478163082946, -1.356846289169558, -1.95765982759828, 0.6658227647012455, 1.14951543846479, -1.335633240404235, -1.324306025670322, 1.286846889860557, 1.223190072096741, -0.6050749036351831, 0.5091449232338207, 1.491509717547662, -2.944393715259336, -7.554129768129437, -4.665208328931745, 1.154866083890913, 1.603245572521532, -0.3710344492354698, 1.376806228050843, 3.256947051444892], 'positive_zeros': ['0.3983715460080655', '1.800903732951002', '2.171857220305130', '3.147860141109490', '3.725845267024700', '4.277842928069599', '5.210070451033466', '5.446898590901368', '6.638201661175068', '6.963473646043995', '7.649381750847242', '8.135338864329198', '8.637514069181490', '9.438106291707603', '9.740971577301442', '10.45447106695392', '10.90412380907866', '11.77841307721365', '12.11630772329132', '12.59369882224626', '13.32252502194307', '13.67071710915938', '14.52832206689048', '14.74387318899473', '15.24561067787523', '15.73679971049382', '16.44489594308262', '16.93665486651844', '17.30163117961139', '17.98101384808464', '18.68169187652863', '18.96735460072153', '19.59452431094073', '19.85086153232992'], 'prelabel': '2-25392-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.239246497354952, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2073482534485997374, 'z1': {'__RealLiteral__': 0, 'data': '0.3983715460080655', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.800903732951002', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.171857220305130', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 202.75614081243526, 'bad_primes': [2, 3, 23], 'central_character': '1.1', 'conductor': 25392, 'conductor_radical': 138, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -5, 0, -1, 0, 2, 0, -4, 0, 0, 0, 0, 0, -4, 0, 1, 0, -5, 0, -4, 0, 0, 0, 0, 0, -10, 0, -5, 0, -5, 0, -8, 0, -1, 0, 4, 0, -7, 0, 2, 0, 11, 0, 0, 0, -4, 0, 4, 0, -1, 0, 0, 0, 5, 0, 4, 0, 0, 0, 12, 0, 3, 0, -4, 0, 0, 0, 4, 0, 1, 0, 16, 0, -2, 0, -5, 0, -9, 0, 0, 0, -4, 0, 4, 0, -5, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 5, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 5, 29], 'euler3': [1, -1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 10, 37], 'euler41': [1, 5, 41], 'euler43': [1, 8, 43], 'euler47': [1, -4, 47], 'euler5': [1, 1, 5], 'euler53': [1, -11, 53], 'euler59': [1, -4, 59], 'euler61': [1, 1, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -12, 71], 'euler73': [1, -3, 73], 'euler79': [1, -4, 79], 'euler83': [1, -16, 83], 'euler89': [1, 9, 89], 'euler97': [1, 5, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 5], [1, 0, 7], [1, 0, 11], [1, 5, 13], [1, -2, 17], [1, 4, 19], [1, 0, 0], [1, 5, 29], [1, 4, 31], [1, 10, 37], [1, 5, 41], [1, 8, 43], [1, -4, 47], [1, -11, 53], [1, -4, 59], [1, 1, 61], [1, -4, 67], [1, -12, 71], [1, -3, 73], [1, -4, 79], [1, -16, 83], [1, 9, 89], [1, 5, 97]], 'index': 4, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25392/v'], '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': '2-25392-1.1-c1-0-4', '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': '2-25392-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.239246497354952, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2073482534485997374, 'z1': {'__RealLiteral__': 0, 'data': '0.3983715460080655', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2073482534485997374', 'Lhash_array': ['2073482534485997374'], 'label': '2-25392-1.1-c1-0-4', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25392/v'}