Formats: - HTML - YAML - JSON - 2026-09-10T16:18:14.966172
  • lfunc_lfunctions • Show schema
    {'Lhash': '510375780900868247299336888701', 'a10': 0, 'a2': 0, 'a3': -1, 'a4': 0, 'a5': -1, 'a6': 0, 'a7': -2, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 59.40869910383263, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [31, [1, 1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '7440.1', 'coefficient_field': '1.1.1.1', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, 2, 7], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 0, 29], [1, 1], [1, 4, 37], [1, 6, 41], [1, 8, 43], [1, -12, 47], [1, 6, 53], [1, -6, 59], [1, -2, 61], [1, 2, 67], [1, -6, 71], [1, -8, 73], [1, 8, 79], [1, 12, 83], [1, 0, 89], [1, 10, 97], [1, 6, 101], [1, -10, 103], [1, 0, 107], [1, -2, 109], [1, 18, 113]], 'euler_factors_factorization': [[1], [[[1, 1], 1]], [[[1, 1], 1]], [[[1, 2, 7], 1]], [[[1, 0, 11], 1]], [[[1, 4, 13], 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'0.40261550052433971362564040935', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '1.73954738745817360051187806680', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '2.77796430070645379020467842410', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 59.40869910383263, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 7440, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -2, 0, 1, 0, 0, 0, -4, 0, 1, 0, 6, 0, -8, 0, 2, 0, 0, 0, 1, 0, -1, 0, 0, 0, -1, 0, 0, 0, 2, 0, -4, 0, 4, 0, -6, 0, -8, 0, -1, 0, 12, 0, -3, 0, -6, 0, -6, 0, 0, 0, 8, 0, 6, 0, 2, 0, -2, 0, 4, 0, -2, 0, 0, 0, 6, 0, 8, 0, -1, 0, 0, 0, -8, 0, 1, 0, -12, 0, -6, 0, 0, 0, 0, 0, 8, 0, 1, 0, 8, 0, -10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 4, 13], 'euler17': [1, -6, 17], 'euler19': [1, 8, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, 1, 0], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, 8, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, -2, 61], 'euler67': [1, 2, 67], 'euler7': [1, 2, 7], 'euler71': [1, -6, 71], 'euler73': [1, -8, 73], 'euler79': [1, 8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 0, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, 2, 7], [1, 0, 11], [1, 4, 13], [1, -6, 17], [1, 8, 19], [1, 0, 23], [1, 0, 29], [1, 1, 0], [1, 4, 37], [1, 6, 41], [1, 8, 43], [1, -12, 47], [1, 6, 53], [1, -6, 59], [1, -2, 61], [1, 2, 67], [1, -6, 71], [1, -8, 73], [1, 8, 79], [1, 12, 83], [1, 0, 89], [1, 10, 97]], 'index': 3, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/7440/b', 'ModularForm/GL2/Q/holomorphic/7440/2/a/b/1/1', 'ModularForm/GL2/Q/holomorphic/7440/2/a/b'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-7440-1.1-c1-0-3', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-7440-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.7077038801339945, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 657769722374118000, 'z1': {'__RealLiteral__': 0, 'data': '0.40261550052433971362564040935', 'prec': 97}}
  • lfunc_instances • Show schema
    • id: 97369
      {'Lhash': '657769722374118000', 'Lhash_array': ['657769722374118000'], 'factors': ['2-7440-1.1-c1-0-3'], 'label': '2-7440-1.1-c1-0-3', 'type': 'ECQ', 'url': 'EllipticCurve/Q/7440/b'}
    • id: 21886689
      {'Lhash': '510375780900868247299336888701', 'Lhash_array': ['510375780900868247299336888701'], 'factors': ['2-7440-1.1-c1-0-3'], 'label': '2-7440-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/b'}
    • id: 24579615
      {'Lhash': '510375780900868247299336888701', 'Lhash_array': ['510375780900868247299336888701'], 'factors': ['2-7440-1.1-c1-0-3'], 'label': '2-7440-1.1-c1-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7440/2/a/b/1/1'}