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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': -2, 'A8': 0, 'A9': 1, 'Lhash': '1135356930376230943', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [-0.7559289460184544, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 145.6471332868155, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '18240.1', 'coefficient_field': '1.1.1.1', 'conductor': 18240, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, 2, 7], [1, -2, 11], [1, -4, 13], [1, -2, 17], [1, -1], [1, 4, 23], [1, 4, 29], [1, 0, 31], [1, 0, 37], [1, 0, 41], [1, -10, 43], [1, -12, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, -16, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -12, 83], [1, 0, 89], [1, 16, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-18240-1.1-c1-0-26', 'leading_term': '3.26259521925', '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/18240/cn', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [3.262595219251256, 2.851715124538538, 1.684286705493549, 0.08058782858383656, -1.274474079510138, -1.611695344128142, -0.6786775798611004, 0.8606346192906997, 1.754901031696618, 1.167234489992308, -0.4684618005641212, -1.685154355477643, -1.341189820471105, 0.1428033123330633, 1.104110585288108, 0.4658222687318676, -0.8173223160535324, -0.5634207717584617, 2.096218000233865, 5.265835124822049, 5.973144721472984, 3.464597534543889, 0.2626169349089775, -0.6037596453894983, 0.898487834136823, 1.939085279979063, 0.6077928165399848, -1.480524765034159, -1.344838840430587, 1.157510540837234, 2.861248019733326, 1.48195743927933, -1.18989609862683, -1.678215446022674, 0.4112047785184348, 2.018944230138397, 1.184427816680047, -0.2441277435470787, 0.1822201997738726, 1.414114631571896, 0.5553072496617413, -2.0911031182168, -2.836509254644281, -0.3269607118525378, 1.618241783079748, -0.725858375365163, -5.066374605537972, -5.917492766704151, -2.491584279415799, 0.2548428547662143, -0.911887890969076, -3.068912154182457, -2.358213713516411, -0.07178352387302186, 0.1216700462380566, -1.439277745864867, -1.440776533785153, 0.07399381297631956, -0.4182550606133009, -3.295301594592543, -4.301360579601366, -1.551475351436919, 0.9428463703038016, -0.1343342854995208, -1.846794884455111, -0.4117553932489425, 1.790999792634011, 0.3517566560886144, -2.842913600948702, -2.234716538266876, 1.735311869915671, 2.933007682250071, -0.2287947951920735, -2.348095101139517, -0.5062185945957205, 1.239336142134328, -0.1353586401347474, -1.233825441286243, 0.8444286116981337, 2.709866608984844, 1.024167406934861, -1.224590653002251, -0.5874285525328301, 0.1936851565763221, -2.179908091196886, -4.489973264173285, -2.707727911573783, 0.07630058410432349, -0.790669822017599, -2.63205397913504, -0.6186653138264008, 2.510903844402937, 1.331693357068845, -1.508093083427198, 0.3307862920347785, 4.850029941589891, 4.882090616499373, 0.9351936908342356, -0.177651463522805, 2.196283598298574, 2.510524322862263, 0.08746232580954816, -0.6021392917479992, 0.611807393911551, 0.3457863368966481, -0.03827477226618079, 2.670939961281097, 5.026631125361688, 2.074948089224952, -2.403096495089719, -1.915685075576486, 0.7469677640899537, -0.7856991343005995, -3.838824503212651, -2.178787638098078, 1.328402174414955, 0.3326538957461335, -2.461202606617167, -1.0276342660477, 1.964328666722503, 1.096372175204828], 'positive_zeros': ['0.7625019381352025', '1.610992132716741', '2.432625847833450', '3.226925497717003', '3.834344614271950', '4.323217502892525', '5.529750653314712', '5.875547358161300', '6.565517126257919', '7.146593574188032', '7.880918150380375', '8.458518573394725', '9.185964860322146', '9.463295539631887', '10.05700441747169', '10.77642048913624', '11.20474978090964', '12.19913902904150', '12.39244100354487', '13.26121139540754', '13.52368046078727', '14.23373186114744', '14.44135435712406', '15.36913737564800', '15.73518697300009', '16.28709969364460', '16.77612065909850', '17.39296537485708', '17.98474529842851', '18.54686778411052', '18.98412645326049', '19.42558007963382'], 'prelabel': '2-18240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.068435411718268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1135356930376230943, 'z1': {'__RealLiteral__': 0, 'data': '0.7625019381352025', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.610992132716741', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.432625847833450', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 145.6471332868155, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 18240, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, -2, 0, 1, 0, 2, 0, 4, 0, 1, 0, 2, 0, 1, 0, -2, 0, -4, 0, 1, 0, 1, 0, -4, 0, 0, 0, 2, 0, -2, 0, 0, 0, 4, 0, 0, 0, 10, 0, 1, 0, 12, 0, -3, 0, 2, 0, 2, 0, 2, 0, 1, 0, -4, 0, -2, 0, -2, 0, 4, 0, 16, 0, -4, 0, 0, 0, -2, 0, 1, 0, -4, 0, -8, 0, 1, 0, 12, 0, 2, 0, -4, 0, 0, 0, -8, 0, 0, 0, 1, 0, -16, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, -4, 13], 'euler17': [1, -2, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 4, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, 0, 37], 'euler41': [1, 0, 41], 'euler43': [1, -10, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -16, 67], 'euler7': [1, 2, 7], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 16, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, 2, 7], [1, -2, 11], [1, -4, 13], [1, -2, 17], [1, -1, 0], [1, 4, 23], [1, 4, 29], [1, 0, 31], [1, 0, 37], [1, 0, 41], [1, -10, 43], [1, -12, 47], [1, -2, 53], [1, 4, 59], [1, 2, 61], [1, -16, 67], [1, 0, 71], [1, 2, 73], [1, 8, 79], [1, -12, 83], [1, 0, 89], [1, 16, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/18240/cn'], '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': '2-18240-1.1-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': '2-18240-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.068435411718268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1135356930376230943, 'z1': {'__RealLiteral__': 0, 'data': '0.7625019381352025', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1135356930376230943', 'Lhash_array': ['1135356930376230943'], 'factors': ['2-18240-1.1-c1-0-26'], 'label': '2-18240-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/18240/cn'}