Formats: - HTML - YAML - JSON - 2026-09-20T17:22:29.825637
  • lfunc_lfunctions • Show schema
    {'A10': 0, 'A2': 1, 'A3': -1, 'A4': -1, 'A5': 0, 'A6': -1, 'A7': 0, 'A8': -3, 'A9': 1, 'Lhash': '356780945455868009', 'a10': [0.0, 0], 'a2': [0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [-0.5, 0], 'a5': [0.0, 0], 'a6': [-0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-1.0606601717798212, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1922.9973066774858, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[3, [1, 1]], [5, [1]], [13, [1]], [19, [1, -1]]], 'bad_primes': [3, 5, 13, 19], 'central_character': '240825.1', 'coefficient_field': '1.1.1.1', 'conductor': 240825, 'conductor_radical': 3705, 'degree': 2, 'euler_factors': [[1, -1, 2], [1, 1], [1], [1, 0, 7], [1, 0, 11], [1], [1, -6, 17], [1, -1], [1, 4, 23], [1, -2, 29], [1, 8, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, -2, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 17, 'label': '2-240825-1.1-c1-0-17', 'leading_term': '2.15384286864', 'load_key': 'Cremona', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'EllipticCurve/Q/240825/bq', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 7}, 'plot_values': [2.153842868636571, 1.344085575457595, -0.3809594427559219, -1.241876043122284, 0.1634763639172985, 2.895247157279531, 3.881012977116482, 1.320804943360073, -2.410355861522667, -2.940307598079375, 0.5629181987571044, 3.927851509546623, 3.401018466403596, 0.6028349332154257, -0.3912228331819713, 0.6888801194459121, 0.6944930466979499, -0.9569072290290335, -1.325638543944653, 0.4262863766498788, 1.40499903957995, 0.4407933822216089, -0.04069087288014621, 0.5081379103537951, -0.6170938107941516, -2.931115610413528, -2.07620542657551, 1.436243843342107, 1.3382561703344, -2.834169365606426, -3.544783915028505, 0.7963834460129842, 1.890583291492389, -2.768689891529303, -4.311536192880103, 0.7264693155486747, 3.603154192498138, 0.4526739602499939, -0.7638745742425262, 2.882225138912901, 3.690978779484895, 0.1298089047515997, -0.02288382664945269, 3.218449081896733, 1.69726795476037, -3.475787314151229, -3.891221521824516, -0.4485771849008471, 0.3058483849025811, -0.3576641255846164, 0.8223228948681229, 0.6522979165770306, -1.611083465220477, -1.03854712289872, 1.507294228718194, 0.8767996777233784, -0.5843280114763816, 0.8860772483971447, 1.207606173082933, -0.8402379732429989, 0.7253781908016949, 4.189468411294346, 1.990550000597894, -1.856557702016945, 0.08105463166268727, 1.969266580648678, -1.241638846018785, -1.60994380473397, 2.803010680796361, 2.776297090697916, -0.7571898163588558, 0.2189480213543782, 1.623652269687993, -1.183921032010415, -0.9967555931427425, 2.591433104445377, 1.156961612098907, -0.1995913615682152, 6.487382068002722, 9.816017869267537, 1.717422136587843, -3.584406168204576, 0.9626737612412445, 3.135449289559418, 0.08993492579954541, 0.2801310369511835, 1.581973450635128, -0.5605829860391001, -1.231899701027159, 0.4504005107109977, 0.1442736382741047, 0.0968391185829738, 1.549056124791739, 0.4932281858728563, -0.956317083854398, 0.05814882747219369, -0.4521673660966446, -0.604426161445683, 3.642936930763152, 3.839559800525989, -2.369724379811813, -1.54003393711029, 5.059232236454578, 3.121002191242479, -0.9096074120634671, 3.58798883815949, 4.726134893202462, -2.497752348069041, -4.021899964223403, 0.05470427906725057, -0.04470744716289425, 0.5119433436784246, 3.164711541708865, 0.1980800330839065, -2.025620462127109, 2.725195328313219, 3.165828191095308, -2.14654021816855, -1.57832096034341, 1.348943896807219, -0.1359725746883627], 'positive_zeros': ['0.4443127558399791', '0.9830974936223205', '1.832123220451570', '2.467590137964769', '3.323977980996247', '3.609949454524708', '4.113887596302248', '4.696578163504022', '5.371279101869549', '5.524173613687345', '5.923729621810463', '6.643393806444784', '7.088685043096862', '7.706088469471329', '8.117848544007903', '8.719028193786285', '9.281527590767685', '9.569648953827147', '10.26095561030236', '10.50205783425754', '11.08032932325141', '11.79729280473272', '12.07645124232765', '12.35775249838551', '12.82426215498061', '13.34200032796782', '13.85425476610889', '14.13884920377724', '14.63809405039885', '14.94942849251280', '15.60170629307364', '15.99457779667151', '16.41905247782321', '16.84689638905499', '17.42900948867832', '17.73042565171143', '18.15813619243558', '18.56615685499271', '19.08514193039532', '19.26564764203160'], 'prelabel': '2-240825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.851993189335026, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 356780945455868009, 'z1': {'__RealLiteral__': 0, 'data': '0.4443127558399791', 'prec': 54}, 'z2': {'__RealLiteral__': 0, 'data': '0.9830974936223205', 'prec': 54}, 'z3': {'__RealLiteral__': 0, 'data': '1.832123220451570', 'prec': 54}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1922.9973066774858, 'bad_primes': [3, 5, 13, 19], 'central_character': '1.1', 'conductor': 240825, 'conductor_radical': 3705, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, -1, 0, -1, 0, -3, 1, 0, 0, 1, 0, 0, 0, -1, 6, 1, 1, 0, 0, 0, -4, 3, 0, 0, -1, 0, 2, 0, -8, 5, 0, 6, 0, -1, -10, 1, 0, 0, 2, 0, 4, 0, 0, -4, 12, 1, -7, 0, -6, 0, 6, -1, 0, 0, -1, 2, 12, 0, -2, -8, 0, 7, 0, 0, -4, -6, 4, 0, 0, -3, 10, -10, 0, -1, 0, 0, 0, 0, 1, 2, 16, 0, 0, 4, -2, 0, 2, 0, 0, 4, 8, 12, 0, -5, 10, -7, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, -1, 0], 'euler2': [1, -1, 2], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 8, 31], 'euler37': [1, 10, 37], 'euler41': [1, -2, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -10, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, -2, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, -1, 2], [1, 1, 0], [1, 0, 0], [1, 0, 7], [1, 0, 11], [1, 0, 0], [1, -6, 17], [1, -1, 0], [1, 4, 23], [1, -2, 29], [1, 8, 31], [1, 10, 37], [1, -2, 41], [1, -4, 43], [1, -12, 47], [1, -6, 53], [1, -12, 59], [1, 2, 61], [1, 4, 67], [1, 0, 71], [1, -10, 73], [1, 0, 79], [1, -16, 83], [1, -2, 89], [1, -10, 97]], 'index': 17, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/240825/bq'], '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': '2-240825-1.1-c1-0-17', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-240825-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 43.851993189335026, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 356780945455868009, 'z1': {'__RealLiteral__': 0, 'data': '0.4443127558399791', 'prec': 54}}
  • lfunc_instances • Show schema
    {'Lhash': '356780945455868009', 'Lhash_array': ['356780945455868009'], 'factors': ['2-240825-1.1-c1-0-17'], 'label': '2-240825-1.1-c1-0-17', 'type': 'ECQ', 'url': 'EllipticCurve/Q/240825/bq'}