-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': -1, 'A9': 0, 'Lhash': '1757621827106315251', 'a10': [0.0, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 276.68164300373667, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '34650.1', 'coefficient_field': '1.1.1.1', 'conductor': 34650, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1, 1], [1], [1], [1, 1], [1, -1], [1, 2, 13], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -2, 61], [1, -4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -12, 83], [1, 6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 71, 'label': '2-34650-1.1-c1-0-71', 'leading_term': '3.80464374769', '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': 1, 'origin': 'EllipticCurve/Q/34650/q', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8637068072134797, 1.216154740556257, 0.7017567333939935, -0.5320264751635413, -1.666194880691242, -1.706134205905264, -0.4620968689183865, 0.9482938080714475, 0.92606141203522, -0.9157194846909896, -2.971447122305295, -3.07414573944521, -1.020650536781838, 0.7410911292021292, -0.3267798912967482, -3.553836398989361, -5.198627935815988, -2.612138413282287, 2.249292900457579, 4.670024624597639, 2.6903321754819, -0.5331145094533566, -0.8119959303235336, 1.716260365371214, 3.125963211844058, 1.349653459178527, -1.059103397809519, -0.9154304520886919, 0.9040040123652167, 1.123263627429788, -0.633673936216433, -1.312223611978891, 0.4943398649964133, 2.118859258832979, 1.112698044585308, -0.7655705541231828, -0.5490647561034327, 0.9739684798027375, 0.832541048317669, -0.7356184636993989, -0.6909387954400281, 1.054146479189794, 0.9779311994702531, -1.704562294010254, -2.876901080231355, -0.3201625025092985, 2.015062379733159, 0.5121267313735125, -1.702385615466808, -0.3239161983803846, 1.878571962339304, -0.4667664798208492, -4.979138711765923, -4.17506291274587, 1.925638435556887, 4.968793994949999, 1.562148737726416, -1.818366104254213, -0.4554723234872925, 1.215122221862905, -1.109749211384497, -3.422783017144969, -1.117582912604268, 2.397562086612489, 2.052591057774166, -0.1792844573688723, -0.2260057875911367, 0.2996648151743408, -1.35766983109271, -2.453058516539669, -0.1064039376328818, 2.218632474177298, 0.852990381235876, -1.17652799813016, -0.2835761357282319, 0.9811930267792256, 0.04534481115089458, -0.04714169776886239, 2.354975092597186, 2.947748759622575, 0.1973183348864248, -0.5729054144443237, 2.269914923103301, 2.692343175412042, -0.789253487740612, -1.229605283625816, 2.844939227249395, 3.565530190258116, -0.71671466403704, -1.35010025681278, 3.664271536561508, 5.16149149919509, 0.5119656714548793, -1.490372392278291, 1.846037810325415, 2.49573555675792, -1.494166048515516, -2.42000550440801, 1.194932087125682, 2.355715868127163, 0.06779133971524107, -0.1789139931426926, 1.185233290674599, -0.04390614142339528, -1.504868693736817, 0.444160311872482, 1.96580090714123, -0.3084483031262192, -1.987579882345205, -0.3888962183121017, 0.4348529071537, -0.2061780390935624, 1.817494694882235, 4.647488509924343, 2.985247151791243, -0.2481504152177704, 0.3783210168677423, 1.598077288472982, -0.1570193471530007, -0.1342530834359761], 'positive_zeros': ['0.9015840789058715', '1.821663939127813', '2.396951428715176', '3.362158187030621', '3.716380921447132', '4.633550076759775', '5.447443294448358', '5.845174216185729', '6.621541016030470', '7.125056610333558', '7.667522759995620', '8.197369782559079', '8.881149377401180', '9.337500437323199', '9.880439218456197', '10.35349317296164', '10.85467727496851', '11.52350288205497', '12.04423090176184', '12.52778946194122', '12.97401092261044', '13.67507249430700', '14.33443891831329', '14.79186090332256', '15.16718340929782', '15.81745909522999', '16.47172177847414', '16.80718700475177', '17.07799354703673', '17.75802305847757', '18.33075711544135', '18.78767667640920', '19.25901140718564', '19.50767833393553'], 'prelabel': '2-34650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.63375011847108, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1757621827106315251, 'z1': {'__RealLiteral__': 0, 'data': '0.9015840789058715', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.821663939127813', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.396951428715176', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 276.68164300373667, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 34650, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 0, 0, -1, -1, 0, 0, 1, 0, -2, 1, 0, 1, 6, 0, -4, 0, 0, -1, 0, 0, 0, 2, 0, -1, -6, 0, -4, -1, 0, -6, 0, 0, -2, 4, 0, 0, -6, 0, 4, 1, 0, 0, 0, 0, 1, 0, 0, -2, 6, 0, 0, 1, 0, 6, 0, 0, 2, 4, 0, 1, 0, 0, 4, 6, 0, 0, 0, 0, -2, 2, 0, -4, -1, 0, 8, 0, 0, 6, 12, 0, 0, -4, 0, -1, -6, 0, 2, 0, 0, 0, 0, 0, -2, -1, 0, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, -4, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, -6, 17], [1, 4, 19], [1, 0, 23], [1, 6, 29], [1, 4, 31], [1, 2, 37], [1, 6, 41], [1, -4, 43], [1, 0, 47], [1, -6, 53], [1, 0, 59], [1, -2, 61], [1, -4, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -12, 83], [1, 6, 89], [1, 2, 97]], 'index': 71, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/34650/q'], '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': '2-34650-1.1-c1-0-71', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-34650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.63375011847108, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1757621827106315251, 'z1': {'__RealLiteral__': 0, 'data': '0.9015840789058715', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1757621827106315251', 'Lhash_array': ['1757621827106315251'], 'label': '2-34650-1.1-c1-0-71', 'type': 'ECQ', 'url': 'EllipticCurve/Q/34650/q'}