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lfunc_lfunctions • Show schema
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{'A10': -4, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 4, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '373800928290988870', 'a10': [-1.2649110640673518, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 91.55647095760013, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '11466.1', 'coefficient_field': '1.1.1.1', 'conductor': 11466, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -4, 5], [1], [1, -4, 11], [1, 1], [1, 2, 17], [1, -4, 19], [1, 2, 23], [1, 6, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 2, 53], [1, -10, 59], [1, -2, 61], [1, 2, 67], [1, -4, 71], [1, 2, 73], [1, -16, 79], [1, 10, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-11466-1.1-c1-0-26', 'leading_term': '2.51112804816', '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/11466/bh', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.511128048155484, 2.250102637759201, 1.493028434775292, 0.4059589204046704, -0.6075513249757207, -1.048930630296862, -0.7003889284166309, 0.06747346827852134, 0.4304322736651075, -0.2333419707041799, -1.618153924749542, -2.441895726798836, -1.417291121314146, 1.382984074233021, 4.075535816884493, 4.229141190308589, 1.058811142909016, -3.466868240665106, -5.995678413791954, -4.708279674763919, -1.031299987050993, 1.734502256522897, 1.653381871971095, -0.0986031765157768, -0.8858012962051748, 0.2210844148153868, 1.489347145929063, 0.9429842483869614, -0.8565427396775611, -1.306649082917348, 0.87929890159072, 3.704976523178173, 4.060071566945861, 1.477523466535003, -1.317316279052638, -1.802112970723537, -0.5346493557773031, 0.1905864777074949, -0.256529301032068, -0.3414861112514526, 0.6851750069311798, 1.14706870107122, -0.5008354968328999, -2.703548303535857, -2.506135448675784, -0.09645164388383004, 0.7309679975607232, -2.191452812752741, -5.70276929465041, -5.163459552775453, -1.02489366471242, 1.461342926383244, -0.5051959955465088, -3.426523610300077, -2.808279872705875, 0.2580180727337177, 1.155844801044054, -0.8562342631720998, -1.595902977578468, 0.9531951013192903, 2.738996558377966, -0.3729361419789263, -5.729989419294095, -7.083190726175781, -3.314188094635212, 0.4514387730293348, 0.5600459141753321, -0.7983895946482695, -0.4484046769961886, 0.6825455742906781, 0.2730760960104243, -0.8091175175096822, -0.4889019936609963, 0.1092584830396165, -1.392112597294918, -3.491763688878105, -2.451059367875116, 1.110477353833263, 2.366318535581581, -0.04741998756981023, -1.74023257302296, -0.01557181039578869, 1.646913443843454, 0.00956751902065544, -1.941298169649491, -0.3128182242637336, 2.515892375909809, 2.06407180156619, -0.1402041952270032, 0.1914653683144811, 0.9081597297596155, -3.916666228739073, -12.20558127432898, -14.03562901633607, -6.079902715161046, 2.647734793631078, 3.67354281163349, 0.01976006960490554, -1.120620355391849, 0.3350825050892068, 0.3081657490602015, -0.7731452780108281, 0.030052208118857, 1.382216532253077, 0.3374926596357697, -1.26183170926772, -0.1539468063640814, 1.482607971198324, -0.2204748872033382, -2.993309438507281, -1.988501370464868, 1.299123520931743, 1.632463295789504, -0.6102939506268626, -0.8858356232246108, 0.6616831409485256, 0.2476220752130498, -1.488258755403616, -1.067415005936066, 0.2260400464090718, -0.7349331184190271], 'positive_zeros': ['0.8412634021820966', '1.726958895111398', '2.195865294904756', '3.138501949592007', '4.058530445603365', '5.072238933736294', '5.735424692226267', '6.215331296653371', '6.881638826826102', '7.424175384039495', '8.365986728836603', '9.123916129300815', '9.394055999514484', '9.853521409006295', '10.44670345040291', '11.26049519567206', '11.59532290323907', '12.56501276066892', '12.96171510394202', '13.72661946075261', '14.15803884928300', '14.67523471130990', '15.23197222043570', '16.20343866133380', '16.59249352437820', '17.08545366856897', '17.55497145052701', '18.13662344827441', '18.30117306157918', '19.17121935974683', '19.74601134721031'], 'prelabel': '2-11466-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.568514563797253, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 373800928290988870, 'z1': {'__RealLiteral__': 0, 'data': '0.8412634021820966', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.726958895111398', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.195865294904756', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 91.55647095760013, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 11466, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 4, 0, 0, -1, 0, -4, 4, 0, -1, 0, 0, 1, -2, 0, 4, 4, 0, -4, -2, 0, 11, 1, 0, 0, -6, 0, -4, -1, 0, 2, 0, 0, 4, -4, 0, -4, 6, 0, -4, 4, 0, 2, 0, 0, 0, -11, 0, -1, -2, 0, 16, 0, 0, 6, 10, 0, 2, 4, 0, 1, -4, 0, -2, -2, 0, 0, 4, 0, -2, -4, 0, 4, 0, 0, 16, 4, 0, -6, -10, 0, -8, 4, 0, -4, -6, 0, 0, -2, 0, 0, 16, 0, -10, 0, 0, 11], 'euler11': [1, -4, 11], 'euler13': [1, 1, 0], 'euler17': [1, 2, 17], 'euler19': [1, -4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 2, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 4, 43], 'euler47': [1, 0, 47], 'euler5': [1, -4, 5], 'euler53': [1, 2, 53], 'euler59': [1, -10, 59], 'euler61': [1, -2, 61], 'euler67': [1, 2, 67], 'euler7': [1, 0, 0], 'euler71': [1, -4, 71], 'euler73': [1, 2, 73], 'euler79': [1, -16, 79], 'euler83': [1, 10, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -4, 5], [1, 0, 0], [1, -4, 11], [1, 1, 0], [1, 2, 17], [1, -4, 19], [1, 2, 23], [1, 6, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 4, 43], [1, 0, 47], [1, 2, 53], [1, -10, 59], [1, -2, 61], [1, 2, 67], [1, -4, 71], [1, 2, 73], [1, -16, 79], [1, 10, 83], [1, 6, 89], [1, 10, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11466/bh'], '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': '2-11466-1.1-c1-0-26', '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': '2-11466-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.568514563797253, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 373800928290988870, 'z1': {'__RealLiteral__': 0, 'data': '0.8412634021820966', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '373800928290988870', 'Lhash_array': ['373800928290988870'], 'factors': ['2-11466-1.1-c1-0-26'], 'label': '2-11466-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11466/bh'}