Formats: - HTML - YAML - JSON - 2026-09-08T10:15:52.891860
  • lfunc_lfunctions • Show schema
    {'Lhash': '1611733051148978817235977913694', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 4, 'a6': 0, 'a7': 3, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 13.798149469277257, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [1]], [3, [1]]], 'bad_primes': [2, 3], 'central_character': '1728.1', 'coefficient_field': '1.1.1.1', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'euler_factors': [[1], [1], [1, -4, 5], [1, -3, 7], [1, 4, 11], [1, 1, 13], [1, -4, 17], [1, 1, 19], [1, -4, 23], [1, 0, 29], [1, -4, 31], [1, -9, 37], [1, 0, 41], [1, 8, 43], [1, 12, 47], [1, 8, 53], [1, 4, 59], [1, -5, 61], [1, -11, 67], [1, -8, 71], [1, -1, 73], [1, -5, 79], [1, 8, 83], [1, 12, 89], [1, -5, 97], [1, 0, 101], [1, 1, 103], [1, 12, 107], [1, -14, 109], [1, 12, 113]], 'euler_factors_factorization': [[1], [1], [[[1, -4, 5], 1]], [[[1, -3, 7], 1]], [[[1, 4, 11], 1]], [[[1, 1, 13], 1]], [[[1, -4, 17], 1]], [[[1, 1, 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0.37426352605395286, 0.11888403141057399, -0.055603475971010174, -0.12594265681656316, -0.07627483882222538, 0.10033537008515517, 0.40099257464591165, 0.8127631513821181, 1.3132006066579551, 1.8715839005369095, 2.4507967500713286], 'positive_zeros': ['1.27143319370400675106679280462917', '2.20593526227161583330529036983721', '3.04682102297854825793595716609707', '4.81675214534703865809257184278861', '5.14803643650686365420219259306497', '5.96792011154325891433457977771168', '6.83361756772483196040188421833757', '7.938743397969043584573887403118830', '8.401866546043067452666777829857290', '9.650456964528158399479426396315682'], 'prelabel': '2-12e3-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.714586042788248, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'trace_hash': 1516555706223705924, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.27143319370400675106679280463', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '2.20593526227161583330529036984', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '3.04682102297854825793595716610', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 13.798149469277257, 'bad_primes': [2, 3], 'central_character': '1.1', 'conductor': 1728, 'conductor_radical': 6, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 4, 0, 3, 0, 0, 0, -4, 0, -1, 0, 0, 0, 4, 0, -1, 0, 0, 0, 4, 0, 11, 0, 0, 0, 0, 0, 4, 0, 0, 0, 12, 0, 9, 0, 0, 0, 0, 0, -8, 0, 0, 0, -12, 0, 2, 0, 0, 0, -8, 0, -16, 0, 0, 0, -4, 0, 5, 0, 0, 0, -4, 0, 11, 0, 0, 0, 8, 0, 1, 0, 0, 0, -12, 0, 5, 0, 0, 0, -8, 0, 16, 0, 0, 0, -12, 0, -3, 0, 0, 0, -4, 0, 5, 0, 0, 0], 'euler11': [1, 4, 11], 'euler13': [1, 1, 13], 'euler17': [1, -4, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -9, 37], 'euler41': [1, 0, 41], 'euler43': [1, 8, 43], 'euler47': [1, 12, 47], 'euler5': [1, -4, 5], 'euler53': [1, 8, 53], 'euler59': [1, 4, 59], 'euler61': [1, -5, 61], 'euler67': [1, -11, 67], 'euler7': [1, -3, 7], 'euler71': [1, -8, 71], 'euler73': [1, -1, 73], 'euler79': [1, -5, 79], 'euler83': [1, 8, 83], 'euler89': [1, 12, 89], 'euler97': [1, -5, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -4, 5], [1, -3, 7], [1, 4, 11], [1, 1, 13], [1, -4, 17], [1, 1, 19], [1, -4, 23], [1, 0, 29], [1, -4, 31], [1, -9, 37], [1, 0, 41], [1, 8, 43], [1, 12, 47], [1, 8, 53], [1, 4, 59], [1, -5, 61], [1, -11, 67], [1, -8, 71], [1, -1, 73], [1, -5, 79], [1, 8, 83], [1, 12, 89], [1, -5, 97]], 'index': 15, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/1728/bb', 'ModularForm/GL2/Q/holomorphic/1728/2/a/bb/1/1', 'ModularForm/GL2/Q/holomorphic/1728/2/a/bb'], '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': '2-12e3-1.1-c1-0-15', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-12e3-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 3.714586042788248, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1516555706223705924, 'z1': {'__RealLiteral__': 0, 'data': '1.27143319370400675106679280463', 'prec': 100}}
  • lfunc_instances • Show schema
    • id: 36276
      {'Lhash': '1516555706223705924', 'Lhash_array': ['1516555706223705924'], 'factors': ['2-12e3-1.1-c1-0-15'], 'label': '2-12e3-1.1-c1-0-15', 'type': 'ECQ', 'url': 'EllipticCurve/Q/1728/bb'}
    • id: 20584871
      {'Lhash': '1611733051148978817235977913694', 'Lhash_array': ['1611733051148978817235977913694'], 'factors': ['2-12e3-1.1-c1-0-15'], 'label': '2-12e3-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/2/a/bb'}
    • id: 24554319
      {'Lhash': '1611733051148978817235977913694', 'Lhash_array': ['1611733051148978817235977913694'], 'factors': ['2-12e3-1.1-c1-0-15'], 'label': '2-12e3-1.1-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1728/2/a/bb/1/1'}