-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1420530794618189231', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 1126.8488733243094, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [7, [1]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '141120.1', 'coefficient_field': '1.1.1.1', 'conductor': 141120, 'conductor_radical': 210, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1], [1, -4, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, -4, 23], [1, -10, 29], [1, -4, 31], [1, -2, 37], [1, -12, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -10, 59], [1, 6, 61], [1, 4, 67], [1, -12, 71], [1, 4, 73], [1, 4, 79], [1, -14, 83], [1, 8, 89], [1, 8, 97]], 'gamma_factors': [[], [0]], 'index': 207, 'label': '2-141120-1.1-c1-0-207', 'leading_term': '4.04636901568', '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/141120/oy', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.046369015675828, 3.277886982931261, 1.424235948129947, -0.237017355403464, -0.3407749526757499, 1.138946573096459, 2.414048974622723, 1.641056568266753, -0.6769221314932725, -1.931445324681716, -0.7326879711641612, 0.8740458512599275, -0.03163059966275512, -2.843119388892431, -3.763777446634104, -1.223578736445226, 1.487167933128764, 0.9864903298663265, -0.9848997546115844, -0.4761860890797228, 1.909369927672462, 1.752862126066923, -1.614118870505625, -3.545695248806492, -1.716936605224248, 0.1426165141434525, -0.812550949521485, -1.466095919738131, 0.8639438392724793, 2.475674658528216, -0.1635892792498318, -3.005935866032657, -0.9486369693083194, 2.831091341251305, 2.407373836809751, -0.3775799391670812, -0.1293887226861519, 1.665683352775091, 0.4289916363521982, -1.680296718411119, -0.3144256538851461, 1.477880436612296, -0.8219682729005287, -3.337570566500004, -1.10555200610636, 1.59887081291544, -0.3728123328406025, -2.655957395698627, -0.5729205997748775, 1.260079220780858, -0.8450183855877863, -1.630984862621506, 1.395525914785923, 1.88805163194504, -1.970568161646971, -3.263027751391389, -0.5733731537737387, 0.07979514565076785, -0.9945399725736567, 1.102276663779998, 3.113689317683377, 0.2432005831399997, -1.795215807518365, 1.98699533855636, 4.547440586021783, 1.196627559111744, -0.9177573337044248, 1.478585893650049, 1.917812557515509, -0.3581666246801153, 0.0957032772165631, 1.012254239102253, -1.522005434767604, -1.582087704259898, 3.827985152912376, 5.954302299778086, 1.777333781282353, -0.4312778441068471, 0.6015139532662765, -0.7934739012838349, -1.216413553086075, 3.710790877848776, 6.322079125978561, 2.164285116414832, -0.5616030752865706, 0.6391573132066533, -0.8479800089101723, -3.17678904248633, -0.9020843672794396, 0.7360851891983077, -1.699985102600965, -1.433671114539506, 1.229743495778161, -0.9667071371698678, -3.382103002975918, 0.9444032960218408, 4.14786289356223, 0.4846094729056088, -1.723021490107475, 0.1742757753043261, -0.06834002165048121, -0.159252797585919, 3.235448237004263, 3.253765473180083, -0.4326754195511554, 0.9746107161987917, 4.344788679729172, 1.629967096846763, -1.157358331606685, 0.8389909730525921, 0.5322524852352398, -1.432805504227294, 1.882595056612137, 4.427283524317453, 0.6285543184297899, -0.8648795143573598, 2.047969557021448, 1.226407947602206, -0.7595432886861907, 1.282048335971813, 1.056872950746087], 'positive_zeros': ['0.7007844686777907', '1.076905989800122', '1.928849533867471', '2.592122659579697', '2.996624862333998', '3.841279565203706', '4.363398530959575', '4.802062994168276', '5.391302846677051', '6.201586789455317', '6.359512707985212', '6.927517246528918', '7.489608667827174', '8.055325881194570', '8.705241399124739', '9.016180552301278', '9.539548776393940', '10.02901040913129', '10.44228176880312', '11.07317437059789', '11.47280125656907', '12.04549662801691', '12.42401876388279', '12.89669187292664', '13.38303995763218', '14.06864665396663', '14.26645780539334', '14.66236613164327', '15.26504490109963', '15.64833055139949', '16.32733354542113', '16.62078989540256', '17.20045263425657', '17.48680727232907', '17.87493273928057', '18.33803848945618', '19.12544863602761', '19.35635318618144', '19.66226762811626'], 'prelabel': '2-141120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.56856972413792, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1420530794618189231, 'z1': {'__RealLiteral__': 0, 'data': '0.7007844686777907', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.076905989800122', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.928849533867471', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1126.8488733243094, 'bad_primes': [2, 3, 5, 7], 'central_character': '1.1', 'conductor': 141120, 'conductor_radical': 210, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 4, 0, -2, 0, 0, 0, 0, 0, -2, 0, 0, 0, 4, 0, 1, 0, 0, 0, 10, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 12, 0, 4, 0, 0, 0, -4, 0, 0, 0, 0, 0, 2, 0, 4, 0, 0, 0, 10, 0, -6, 0, 0, 0, -2, 0, -4, 0, 0, 0, 12, 0, -4, 0, 0, 0, 0, 0, -4, 0, 0, 0, 14, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, -2, 0, -8, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, -4, 23], 'euler29': [1, -10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, -12, 41], 'euler43': [1, -4, 43], 'euler47': [1, 4, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -10, 59], 'euler61': [1, 6, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -12, 71], 'euler73': [1, 4, 73], 'euler79': [1, 4, 79], 'euler83': [1, -14, 83], 'euler89': [1, 8, 89], 'euler97': [1, 8, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, 0, 0], [1, -4, 11], [1, 2, 13], [1, 0, 17], [1, 2, 19], [1, -4, 23], [1, -10, 29], [1, -4, 31], [1, -2, 37], [1, -12, 41], [1, -4, 43], [1, 4, 47], [1, -2, 53], [1, -10, 59], [1, 6, 61], [1, 4, 67], [1, -12, 71], [1, 4, 73], [1, 4, 79], [1, -14, 83], [1, 8, 89], [1, 8, 97]], 'index': 207, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/141120/oy'], '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': '2-141120-1.1-c1-0-207', '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': '2-141120-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 33.56856972413792, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1420530794618189231, 'z1': {'__RealLiteral__': 0, 'data': '0.7007844686777907', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1420530794618189231', 'Lhash_array': ['1420530794618189231'], 'label': '2-141120-1.1-c1-0-207', 'type': 'ECQ', 'url': 'EllipticCurve/Q/141120/oy'}