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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': '1212975552281331811', '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, -5, 11], [1, -4, 13], [1, 2, 17], [1, 0, 19], [1], [1, 1, 29], [1, -3, 31], [1, -4, 37], [1, 0, 41], [1, 2, 43], [1, -8, 47], [1, -9, 53], [1, -7, 59], [1, -4, 61], [1, 8, 67], [1, 10, 71], [1, 3, 73], [1, -3, 79], [1, -3, 83], [1, -10, 89], [1, -17, 97]], 'gamma_factors': [[], [0]], 'index': 8, 'label': '2-12696-1.1-c1-0-8', 'leading_term': '2.83310972939', '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/12696/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.833109729387842, 2.537716684549344, 1.688901729571913, 0.4984206455533936, -0.5437496878077196, -0.8524375775959666, -0.2050821572266599, 0.8863910609404897, 1.33447363238999, 0.2626729507940863, -2.100691618252367, -4.279338043887723, -4.563633018928674, -2.519984966202286, 0.3947032710812925, 1.942614657357713, 1.137479309622037, -0.7568888222228354, -1.448785094446648, 0.0119134826123751, 2.213061036418804, 2.943763497217188, 1.686428080822883, 0.1371374074791237, 0.04609504233776675, 0.9935960414665626, 1.01968531383406, -0.5099261062088051, -1.575518267343639, 0.1190509641178397, 3.782502445276616, 5.77238672078353, 3.757340521814262, -0.2390774059156128, -2.086035667423984, -0.5370983772197154, 1.462471835083557, 0.9295963748607944, -1.146571065820087, -1.446757326589615, 0.7509917177204547, 2.457585169281292, 1.331600330351201, -0.8787372970329926, -0.9656256168749278, 0.9448556369094827, 1.752022712053051, 0.4166747140313132, -0.2035046717686565, 2.115513463604029, 4.993444721976833, 4.586187820951748, 1.378479862567895, -0.4346788167187196, 0.6977847292798809, 1.507088517569635, -0.5310721559960647, -2.821797517254562, -1.821473710928778, 0.7823736794755859, 0.2558377179187073, -3.566594676639382, -5.493415134015495, -2.774097008369875, 0.7123658250169304, 0.5371204571328295, -1.738764667827328, -1.820229407230226, 0.2637968515842601, 1.040324072945898, 0.05608556683734637, 0.1983140870264403, 1.66998984524869, 1.172363676411342, -1.607177090908139, -2.209353084279032, 1.151422292621248, 3.51883412367143, 0.7544768558481412, -3.269229017104617, -2.525005725656581, 1.472985111578504, 2.379994616288141, -0.5413033184975888, -1.943991386225835, 0.04254759866586835, 1.263100864592875, -0.3164449429635649, -1.213053041057166, 0.4076681309332355, 1.093670320687528, -0.9322534473710828, -1.725356915164133, 1.119344014807047, 3.329002782257226, 1.285729014823201, -1.258939021774084, 0.182600396555974, 2.819259104300638, 2.001004726070228, -0.2480547582060118, 0.265590507393177, 1.286844244477252, -1.473063226890254, -4.998325091703931, -3.373623670368022, 1.209881793917749, 1.618617044444269, -1.953900495759656, -2.926380977276078, -0.3344728873528824, 0.4196724947425197, -1.638306061437223, -1.875476932821355, 0.1804783913954791, 0.07590020158272925, -2.148902489376512, -1.764706265014395, 1.090109585511032, 1.603965030240505, -0.03093502826001923], 'positive_zeros': ['0.8565383517966445', '1.548268233705654', '2.283404228804247', '3.463004611790009', '4.147464993010050', '4.748658304972288', '5.791461877646404', '5.982612574921075', '6.679479796421248', '7.240398434963280', '8.233377211300098', '8.804231395116648', '9.360773641906249', '9.928085466447988', '10.63871466078352', '11.13497366313442', '11.82190776666198', '12.04461182149160', '13.13435870457426', '13.39419936958970', '13.95391028670079', '14.66147283549408', '15.02182116515789', '15.92995392768628', '16.31034807325036', '16.96765427994913', '17.51698171267489', '17.70208268809889', '18.36167561082006', '18.92910767785441', '19.54004410469710'], 'prelabel': '2-12696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.068667757266482, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1212975552281331811, 'z1': {'__RealLiteral__': 0, 'data': '0.8565383517966445', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.548268233705654', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.283404228804247', '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, 5, 0, 4, 0, -2, 0, -2, 0, 0, 0, -1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 3, 0, -5, 0, 2, 0, 4, 0, -4, 0, 0, 0, -2, 0, 2, 0, 8, 0, -6, 0, 2, 0, 9, 0, 10, 0, 0, 0, 7, 0, 4, 0, 1, 0, 8, 0, -8, 0, 0, 0, -10, 0, -3, 0, 1, 0, 5, 0, 3, 0, 1, 0, 3, 0, -4, 0, 1, 0, 10, 0, 4, 0, -3, 0, 0, 0, 17, 0, 5, 0], 'euler11': [1, -5, 11], 'euler13': [1, -4, 13], 'euler17': [1, 2, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 1, 29], 'euler3': [1, 1, 0], 'euler31': [1, -3, 31], 'euler37': [1, -4, 37], 'euler41': [1, 0, 41], 'euler43': [1, 2, 43], 'euler47': [1, -8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -9, 53], 'euler59': [1, -7, 59], 'euler61': [1, -4, 61], 'euler67': [1, 8, 67], 'euler7': [1, -1, 7], 'euler71': [1, 10, 71], 'euler73': [1, 3, 73], 'euler79': [1, -3, 79], 'euler83': [1, -3, 83], 'euler89': [1, -10, 89], 'euler97': [1, -17, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -2, 5], [1, -1, 7], [1, -5, 11], [1, -4, 13], [1, 2, 17], [1, 0, 19], [1, 0, 0], [1, 1, 29], [1, -3, 31], [1, -4, 37], [1, 0, 41], [1, 2, 43], [1, -8, 47], [1, -9, 53], [1, -7, 59], [1, -4, 61], [1, 8, 67], [1, 10, 71], [1, 3, 73], [1, -3, 79], [1, -3, 83], [1, -10, 89], [1, -17, 97]], 'index': 8, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/12696/m'], '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-c1-0-8', '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': '2-12696-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 10.068667757266482, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1212975552281331811, 'z1': {'__RealLiteral__': 0, 'data': '0.8565383517966445', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1212975552281331811', 'Lhash_array': ['1212975552281331811'], 'label': '2-12696-1.1-c1-0-8', 'type': 'ECQ', 'url': 'EllipticCurve/Q/12696/m'}