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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -4, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '1651922357699575201', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 92.75422698791934, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 11], 'central_character': '11616.1', 'coefficient_field': '1.1.1.1', 'conductor': 11616, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 4, 5], [1, 2, 7], [1], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -8, 43], [1, 10, 47], [1, 12, 53], [1, 0, 59], [1, 8, 61], [1, 4, 67], [1, 6, 71], [1, 10, 73], [1, 6, 79], [1, 12, 83], [1, 14, 89], [1, 18, 97]], 'gamma_factors': [[], [0]], 'index': 28, 'label': '2-11616-1.1-c1-0-28', 'leading_term': '4.35525131709', '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': 2, 'origin': 'EllipticCurve/Q/11616/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.2668875292126405, -0.9893351132023337, -1.861596729339021, -2.299254329467312, -1.65655364423203, 0.2961678835768785, 2.968297032824385, 5.058294900116177, 5.320741759203753, 3.547482617496099, 0.9288162743402394, -0.7206331948035233, -0.4153404876794126, 1.127859828915444, 2.150208965578298, 1.586693452464118, 0.1844050669227747, -0.2897142583382249, 0.9111516898406168, 2.442280417274792, 2.186006661405525, -0.2708261315646657, -2.839391721244878, -3.021507552021117, -0.7149461537451507, 1.595269325684267, 1.691283034839828, 0.1740465281845055, -0.4991899420357593, 0.6445515589989042, 1.748089486314989, 0.7552740155805481, -1.372494745681066, -1.455862600442933, 1.665252203882231, 5.050684137949077, 4.996520128813046, 1.791311015035128, -0.5037595559602772, 0.7376978696331598, 3.38293608628169, 3.609530581126719, 1.098265033158948, -0.8516076274895579, -0.1822155148031253, 1.289010263801343, 1.097252830652482, -0.08296395133425563, -0.06295607724610491, 0.6549013110201644, -0.6167387279434116, -3.755825426184133, -4.580670327416797, -0.5842062731239822, 4.463578445892092, 4.793270899228759, 0.4701996700396855, -2.649133046447317, -1.047277279364801, 2.09653284385698, 2.338948836295818, 0.3330304949611307, -0.395665027449536, 0.4153579518829147, 0.1610396365987131, -1.04350497138212, -0.0216937661546962, 3.448002974080314, 4.977072279850262, 2.244161076676937, -0.7372703100942315, 0.4489551250041047, 3.652864149763725, 3.661427886833852, 0.4893119987151226, -1.191464798834191, -0.01600312659827317, 0.5565860298164839, -0.80055226542189, -0.9691689717762145, 0.8544379391424565, 0.1605140478195455, -5.170011364070234, -9.39681749809286, -6.583717149572513, 0.1299282842211702, 3.072537095501145, 1.1220418988356, -0.4779909872845139, 0.311448051304821, 0.3365199758456848, -1.366222680183277, -1.657202322860963, 0.09073244075936635, 0.4718962855746783, -1.106405371814565, -1.046400389418339, 0.7020934314452647, -0.9568536143355681, -6.635674768496685, -8.954262460894865, -3.745172840743021, 2.420699754080535, 2.192913358188604, -1.591249185516252, -2.124421650484303, 0.05278492041664233, 0.1623660056646768, -1.232906243199161, -0.5264066389792404, 0.8320372756688125, -0.7348638426368937, -3.091055585020011, -2.050826860842631, 0.2464280354050407, -0.6560677195196102, -2.436413965097672, -0.2095300663328132, 3.366609686596461, 2.194084883752607], 'positive_zeros': ['1.469594719271071', '2.858659362367730', '3.326454111153154', '4.290969934888775', '4.595246988928372', '5.477367978109670', '6.314197632961270', '7.030539555470152', '7.392585089103402', '8.086118540590009', '8.639510000465844', '9.654631866288956', '9.920266811190632', '10.85570296891418', '11.27766505245713', '11.97671463764802', '12.26953340210574', '12.68370158403257', '13.52579861028912', '14.27488420382222', '14.82560142242255', '15.55064256768918', '15.88056385479245', '16.28272737799618', '16.75199081851267', '17.65842322140401', '17.96145388450153', '18.79066859882093', '19.25261590323862', '19.62060230625918'], 'prelabel': '2-11616-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.630899593907069, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1651922357699575201, 'z1': {'__RealLiteral__': 0, 'data': '1.469594719271071', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.858659362367730', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.326454111153154', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 92.75422698791934, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 11616, 'conductor_radical': 66, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -4, 0, -2, 0, 1, 0, 0, 0, -4, 0, 4, 0, -2, 0, 4, 0, 2, 0, -6, 0, 11, 0, -1, 0, 6, 0, -4, 0, 0, 0, 8, 0, -2, 0, 4, 0, -6, 0, 8, 0, -4, 0, -10, 0, -3, 0, 2, 0, -12, 0, 0, 0, -4, 0, 0, 0, -8, 0, -2, 0, 16, 0, -4, 0, 6, 0, -6, 0, -10, 0, -11, 0, 0, 0, -6, 0, 1, 0, -12, 0, 8, 0, -6, 0, -14, 0, 8, 0, 4, 0, -16, 0, -18, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 4, 13], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 10, 47], 'euler5': [1, 4, 5], 'euler53': [1, 12, 53], 'euler59': [1, 0, 59], 'euler61': [1, 8, 61], 'euler67': [1, 4, 67], 'euler7': [1, 2, 7], 'euler71': [1, 6, 71], 'euler73': [1, 10, 73], 'euler79': [1, 6, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, 18, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 4, 5], [1, 2, 7], [1, 0, 0], [1, 4, 13], [1, 2, 17], [1, -4, 19], [1, 6, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -8, 43], [1, 10, 47], [1, 12, 53], [1, 0, 59], [1, 8, 61], [1, 4, 67], [1, 6, 71], [1, 10, 73], [1, 6, 79], [1, 12, 83], [1, 14, 89], [1, 18, 97]], 'index': 28, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11616/a'], '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': '2-11616-1.1-c1-0-28', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 2, 'prelabel': '2-11616-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.630899593907069, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1651922357699575201, 'z1': {'__RealLiteral__': 0, 'data': '1.469594719271071', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1651922357699575201', 'Lhash_array': ['1651922357699575201'], 'factors': ['2-11616-1.1-c1-0-28'], 'label': '2-11616-1.1-c1-0-28', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11616/a'}