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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1031120770184667251', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 215.02116256290392, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [11, [1, -1]], [17, [1, 1]]], 'bad_primes': [2, 3, 11, 17], 'central_character': '26928.1', 'coefficient_field': '1.1.1.1', 'conductor': 26928, 'conductor_radical': 1122, 'degree': 2, 'euler_factors': [[1], [1], [1, 2, 5], [1, 0, 7], [1, -1], [1, 2, 13], [1, 1], [1, 8, 19], [1, 8, 23], [1, 6, 29], [1, 8, 31], [1, -6, 37], [1, 2, 41], [1, 8, 43], [1, 4, 47], [1, 6, 53], [1, 8, 59], [1, -10, 61], [1, 4, 67], [1, 0, 71], [1, 10, 73], [1, 0, 79], [1, -12, 83], [1, -14, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 52, 'label': '2-26928-1.1-c1-0-52', 'leading_term': '7.42058288995', '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/26928/o', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.4527866681866683, -1.659524234270848, -3.086252354878598, -3.858201754109967, -3.262672881479334, -1.465355126945232, 0.3001644644674704, 0.5645649916986171, -1.0063378562742, -3.021125605671214, -3.452535116252439, -1.63295936616601, 0.9057353292963953, 1.933901550597235, 0.9640100094192652, -0.2010427524212709, 0.2728683277564237, 1.77185493669721, 1.82874625669301, -0.5740839848981184, -3.181782658284777, -2.938104413916189, 0.03469348123986366, 2.288002886530466, 1.384034027878529, -0.8929894282895264, -1.002399336533351, 1.415878560910015, 3.097693129420387, 1.937946580928802, -0.0003334515432362245, 0.1779763925283208, 1.578676624011442, 0.942189571094151, -1.860670639010036, -3.073585605755305, -0.8107834144767434, 1.571464395618338, 0.3435658876591687, -2.696389371340512, -2.804295420341514, 0.3541325627141174, 2.24510863349507, 0.7020859842222208, -0.9163370522084199, 0.302980650355025, 1.96920609489383, 0.9036371438354587, -1.003169468701885, -0.1280983866021152, 2.107527569259168, 1.449065143127675, -1.280848028731429, -0.8061909412109555, 3.562193070223277, 6.004608236561237, 3.342691460001976, -0.1570292052115696, -0.4089766220794482, 0.09581036554829282, -1.885093471092256, -3.679118539280952, -1.757354110001261, 1.181914086343718, 0.8897984869675799, -0.5466494946056561, 1.179544087887166, 3.936022441617553, 2.773366962447816, -0.401211464459507, 0.2970157005244084, 3.884841460629216, 3.996376804212807, 0.370441755011189, -0.9290361464579499, 1.321392220733014, 2.085093612839905, 0.2385145107165173, 0.05017974269857286, 1.773752530751846, 1.124238932850086, -1.003771671938925, 0.9123577870947513, 5.755161902359304, 6.245405448952399, 1.776964724698288, -0.7493160379976873, 0.1709577404709575, -0.9716459596127659, -4.530431755428291, -4.521199726759843, -0.6268439304708489, 1.074918130302098, -0.1480971530407339, 0.4704532728391994, 2.30827614703034, 0.949543188635194, -1.165258657109031, 1.319292179006368, 5.035579199765968, 3.365844096474523, -0.7172632331511245, -0.5519920541476242, 1.182306138534552, -1.301622384822618, -4.583141944911213, -3.023469589082216, -0.07924894854530522, -0.650399423687057, -1.482140246249181, 0.429594390127728, 1.00038425080726, -0.807418012517158, 0.9204049116096737, 6.123607555322812, 6.684995621607385, 1.906253855853268, 0.07155741581103428, 2.360411965825677, 2.116136807575269], 'positive_zeros': ['1.695366559687323', '2.118450181480476', '3.153689417239445', '3.931811322910601', '4.191625766484804', '4.952880785892710', '5.747360738628106', '6.392765943279498', '6.869852626693579', '7.749926322631088', '7.962465377364814', '8.592448746574907', '9.314473678031908', '9.778266110626677', '10.47412501154616', '11.07587641651604', '11.46451166520805', '12.09843954661148', '12.51367122730175', '13.12658311318383', '13.55721258031928', '14.48182147083148', '14.85569180645415', '15.02887765900210', '15.87955012115545', '16.36982758896786', '16.64185702606004', '17.45632941086915', '17.72464494745940', '18.52853420705812', '18.87213490399938', '19.53939848406687', '19.74059154374764'], 'prelabel': '2-26928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.663599918263724, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1031120770184667251, 'z1': {'__RealLiteral__': 0, 'data': '1.695366559687323', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.118450181480476', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '3.153689417239445', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 215.02116256290392, 'bad_primes': [2, 3, 11, 17], 'central_character': '1.1', 'conductor': 26928, 'conductor_radical': 1122, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, -1, 0, -8, 0, 0, 0, -8, 0, -1, 0, 0, 0, -6, 0, -8, 0, 0, 0, 0, 0, 6, 0, 0, 0, -2, 0, -8, 0, 0, 0, -4, 0, -7, 0, 0, 0, -6, 0, -2, 0, 0, 0, -8, 0, 10, 0, 0, 0, 4, 0, -4, 0, 0, 0, 0, 0, -10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 2, 0, 0, 0, 14, 0, 0, 0, 0, 0, 16, 0, -14, 0, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 1, 0], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 8, 43], 'euler47': [1, 4, 47], 'euler5': [1, 2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 8, 59], 'euler61': [1, -10, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, 10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -12, 83], 'euler89': [1, -14, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 2, 5], [1, 0, 7], [1, -1, 0], [1, 2, 13], [1, 1, 0], [1, 8, 19], [1, 8, 23], [1, 6, 29], [1, 8, 31], [1, -6, 37], [1, 2, 41], [1, 8, 43], [1, 4, 47], [1, 6, 53], [1, 8, 59], [1, -10, 61], [1, 4, 67], [1, 0, 71], [1, 10, 73], [1, 0, 79], [1, -12, 83], [1, -14, 89], [1, 14, 97]], 'index': 52, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/26928/o'], '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': '2-26928-1.1-c1-0-52', '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': '2-26928-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.663599918263724, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1031120770184667251, 'z1': {'__RealLiteral__': 0, 'data': '1.695366559687323', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1031120770184667251', 'Lhash_array': ['1031120770184667251'], 'label': '2-26928-1.1-c1-0-52', 'type': 'ECQ', 'url': 'EllipticCurve/Q/26928/o'}