-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 1, 'A3': -1, 'A4': 1, 'A5': 0, 'A6': -1, 'A7': 4, 'A8': 1, 'A9': 1, 'Lhash': '2152914081989070835', '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': [1.5118578920369088, 0], 'a8': [0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2911.7449097059907, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1, 1]], [5, [1]], [11, [1, -1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 11, 13, 17], 'central_character': '364650.1', 'coefficient_field': '1.1.1.1', 'conductor': 364650, 'conductor_radical': 72930, 'degree': 2, 'euler_factors': [[1, -1], [1, 1], [1], [1, -4, 7], [1, -1], [1, 1], [1, 1], [1, -2, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, 2, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, 4, 61], [1, -16, 67], [1, -12, 71], [1, -4, 73], [1, -8, 79], [1, -12, 83], [1, -6, 89], [1, 14, 97]], 'gamma_factors': [[], [0]], 'index': 140, 'label': '2-364650-1.1-c1-0-140', 'leading_term': '14.3969829028', '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/364650/ey', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 3.208704304362806, 4.337479591456643, 2.743680473007198, 0.2245521706623555, -0.398051889050648, 1.356816884874937, 2.734192248570372, 1.583368476245486, -0.0437926383616438, 1.353012850220705, 4.84351103396463, 5.572594338926909, 2.050777008983229, -1.187661668883823, -0.5439902449061468, 1.296386619687814, 0.5989074472848515, -1.120558253225241, -0.8331904658050685, 0.1677768698988746, -0.2253339066299663, -0.006336642734542462, 2.258268842993738, 2.998443507863156, 0.390320052157326, -0.9906417480471734, 0.9927751718525677, 1.100987936473264, -2.451011126024755, -3.316674764355123, -0.02696386847966638, 0.3964373097031027, -1.977285205445824, 1.515561420763517, 8.851682362037613, 7.910949335783919, 0.175234504400855, -0.4636955848178293, 5.912440172974338, 6.26624822191177, 0.3230284876448775, -1.177154061584027, 1.51830221486389, 1.118799964621629, -0.5723955351217179, 0.2322802249395682, 0.1864460847859485, -1.243745325583501, -0.1941299027684244, 0.4340753229932652, -2.959267508780628, -4.275881767486281, -0.333388990149594, 1.534754259309505, -0.3281039063665977, 0.4353962225364036, 2.196190855305888, 0.2519218215165414, -0.72837256466533, 1.493234839968206, 0.9798032215997214, -0.6132449436461124, 2.198031931574075, 3.031617614032428, -2.250254500426354, -3.846824163507221, 0.4220183138867698, 1.029111206307885, -0.6443031053112549, 1.212431183981786, 0.4480075774823522, -3.510826827612272, -1.02599148125019, 3.034250315924699, -0.7428299863181528, -1.922390691960033, 5.362346642127182, 5.726696721757112, -2.982469295458303, -4.662596958925457, -0.1945143345834537, -0.4487286315535838, -0.9566303842191247, 1.879800201344248, 1.488008028528954, -0.159781078053723, 1.504585280329652, 1.29896199869724, -0.7446551504471604, 0.5585124743405033, 0.8496041656567797, -1.725581448097077, -0.714255267235857, 1.408687925606565, -0.2540067562713668, -0.6665759327219161, 0.5051509162679478, -0.5694740368457784, 0.4429417624818153, 1.694006400947258, -2.674375249791266, -1.572172163687231, 9.003030682179423, 9.703067713968572, -0.03061035129490565, -0.4165783619532969, 3.519992787859486, -0.552161853368963, -1.940130717207443, 1.855926278253319, -0.0298940781102154, -1.492633406521787, 2.403157973756763, 1.556297790834387, -0.7978202984712652, 2.621174166829034, 2.071125900993014, -3.157917748083704, -2.341400173236448, 0.1084182189332107], 'positive_zeros': ['1.030881580578906', '1.331422544974703', '2.231855622646196', '2.332642564049252', '3.377853988237144', '3.811898630151182', '4.325639208963494', '4.929088192009698', '5.170049773825811', '5.501078921719667', '6.284079256783595', '6.645227773488032', '7.090076911456127', '7.752252405186998', '8.039942189700306', '8.442531550460307', '9.257337354421746', '9.522519870450280', '10.26646280579916', '10.60914182635491', '11.12948083220973', '11.45335977101676', '11.78106796597090', '12.27488182533760', '12.55089181335320', '13.26996070502926', '13.70066829897014', '13.95205364876455', '14.52378570777108', '14.84281990623697', '15.35040726339709', '15.59372043172531', '16.15462174400095', '16.72329884546160', '17.11125412514286', '17.37314957338050', '17.77757403095448', '18.29406769655814', '18.71612119695493', '19.07999716343387', '19.66361116275199'], 'prelabel': '2-364650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.96058663233741, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2152914081989070835, 'z1': {'__RealLiteral__': 0, 'data': '1.030881580578906', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.331422544974703', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.231855622646196', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2911.7449097059907, 'bad_primes': [2, 3, 5, 11, 13, 17], 'central_character': '1.1', 'conductor': 364650, 'conductor_radical': 72930, 'degree': 2, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, 4, 1, 1, 0, 1, -1, -1, 4, 0, 1, -1, 1, 2, 0, -4, 1, 0, -1, 0, -1, -1, 4, -6, 0, 8, 1, -1, -1, 0, 1, -2, 2, 1, 0, -6, -4, -2, 1, 0, 0, 6, -1, 9, 0, 1, -1, -6, -1, 0, 4, -2, -6, 6, 0, -4, 8, 4, 1, 0, -1, 16, -1, 0, 0, 12, 1, 4, -2, 0, 2, 4, 1, 8, 0, 1, -6, 12, -4, 0, -2, 6, 1, 6, 0, -4, 0, -8, 6, 0, -1, -14, 9, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, -2, 19], 'euler2': [1, -1, 0], 'euler23': [1, 0, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 2, 43], 'euler47': [1, -6, 47], 'euler5': [1, 0, 0], 'euler53': [1, 6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 4, 61], 'euler67': [1, -16, 67], 'euler7': [1, -4, 7], 'euler71': [1, -12, 71], 'euler73': [1, -4, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, -6, 89], 'euler97': [1, 14, 97], 'euler_factors': [[1, -1, 0], [1, 1, 0], [1, 0, 0], [1, -4, 7], [1, -1, 0], [1, 1, 0], [1, 1, 0], [1, -2, 19], [1, 0, 23], [1, 6, 29], [1, -8, 31], [1, 2, 37], [1, 6, 41], [1, 2, 43], [1, -6, 47], [1, 6, 53], [1, -6, 59], [1, 4, 61], [1, -16, 67], [1, -12, 71], [1, -4, 73], [1, -8, 79], [1, -12, 83], [1, -6, 89], [1, 14, 97]], 'index': 140, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/364650/ey'], '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': '2-364650-1.1-c1-0-140', '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': '2-364650-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 53.96058663233741, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2152914081989070835, 'z1': {'__RealLiteral__': 0, 'data': '1.030881580578906', 'prec': 57}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2152914081989070835', 'Lhash_array': ['2152914081989070835'], 'label': '2-364650-1.1-c1-0-140', 'type': 'ECQ', 'url': 'EllipticCurve/Q/364650/ey'}