-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '2126746618887898698', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 581.5345078405811, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1, -1]], [17, [1]]], 'bad_primes': [2, 3, 7, 17], 'central_character': '72828.1', 'coefficient_field': '1.1.1.1', 'conductor': 72828, 'conductor_radical': 714, 'degree': 2, 'euler_factors': [[1], [1], [1, -2, 5], [1, -1], [1, 0, 11], [1, -6, 13], [1], [1, 2, 19], [1, 0, 23], [1, -8, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -8, 43], [1, -8, 47], [1, -2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 8, 73], [1, -8, 79], [1, 0, 83], [1, 10, 89], [1, 12, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-72828-1.1-c1-0-13', 'leading_term': '4.08197780159', '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/72828/y', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.081977801594503, 3.409368467816239, 1.668941251018208, -0.2490899027248782, -1.133975248977673, -0.4392361072903793, 0.931275007702665, 1.278029336051178, -0.02476357510024533, -1.508818288840796, -1.117602576815675, 1.085428317986418, 2.4856417317774, 0.97528352683365, -2.052514015403667, -3.104811714391971, -1.173574455270966, 0.673603190939748, -0.5600689223070274, -3.424656808543948, -3.958435632742119, -1.457605863552838, 0.5574869782497537, -0.1763730620124148, -1.342148783194894, -0.3380482085835768, 0.9372835705293768, -0.7033699531515107, -3.52009383695657, -2.725766649977071, 1.618473202124875, 3.94638229299563, 1.75528351326177, -0.6214471359340228, 0.4564369305051296, 2.068094046536867, 0.6757615897722343, -1.09756120969072, 0.579945166623715, 3.198902769905483, 2.142418812909982, -0.8551718552749704, -1.009419200490603, 0.5528062086919375, -0.5408450851987064, -2.63577973544475, -0.7481670952202958, 3.1577888436293, 2.685294941447032, -1.235610003372825, -1.737714685360287, 1.463418434473447, 2.058995451033139, -0.7505477119561121, -1.616344135606221, -0.01096698705777257, -0.1217451895013677, -0.8410367319852479, 2.009857044858795, 5.32530782715872, 3.158715870029698, -1.356966224759918, -1.378938851047844, 0.6933431310805596, -1.107970016305896, -3.595694908924417, -1.059954774730463, 2.504601484953813, 1.15903525713458, -1.441583567685263, -0.4031168249171308, 0.7729001581159964, -0.7020716342518036, -0.4577125289644235, 2.241293227662478, 1.599581455733041, -1.533772704254991, 0.0292225340551768, 4.230772386113798, 2.540836311736382, -2.792815290093844, -2.99339402584344, 0.2307504334456785, -0.007887094655987671, -1.554052142523544, -0.3380999910074502, 0.01233116510893961, -1.744475991235273, -0.03054924181274332, 3.989723612821328, 2.670154897526957, -1.777759069382885, -1.205489869658643, 1.666787952069606, 0.5016344838670813, -0.1648253982225344, 3.776139643044074, 5.144676385517292, 0.7323328890741966, -1.526781469161436, 0.4755552704689135, 0.2681656738884572, -1.49647163070337, -0.2042252185241798, 0.3179762071201056, -2.391028780563405, -1.520279761953718, 3.172372948899567, 2.441209135736879, -2.658102131620228, -2.67008248939806, 0.227634049906622, -0.9853630144180788, -1.840975967807778, 1.674523440649767, 2.868340504958863, 0.2507985138380876, 0.6090926622011162, 2.094022860146236, -0.967484722393151, -3.225600338945411], 'positive_zeros': ['0.7125986581304658', '1.328893009972771', '1.996518212710818', '2.637354688048276', '3.330511958101592', '4.122329016023037', '4.442466329813545', '5.392498879832578', '5.721817018846233', '6.296297486186707', '6.686632604404810', '7.412138415575014', '8.148034237227246', '8.446361516442434', '9.068422916325807', '9.450709140111622', '10.16707547304933', '10.64136379185375', '10.94115086400176', '11.54475863572892', '12.16710739930725', '12.64043199326678', '13.18557983985612', '13.75219307620529', '13.97430800612745', '14.36561042076394', '15.15971101164468', '15.63676547185901', '15.91088368668310', '16.55849371250921', '17.08734389380381', '17.54777370669957', '17.90064699494123', '18.29610733425498', '18.86478695115092', '19.24832323886449', '19.86164808595008'], 'prelabel': '2-72828-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.11502659838013, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2126746618887898698, 'z1': {'__RealLiteral__': 0, 'data': '0.7125986581304658', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.328893009972771', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.996518212710818', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 581.5345078405811, 'bad_primes': [2, 3, 7, 17], 'central_character': '1.1', 'conductor': 72828, 'conductor_radical': 714, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 1, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -1, 0, 0, 0, 8, 0, 0, 0, 0, 0, 2, 0, -2, 0, 0, 0, 2, 0, 8, 0, 0, 0, 8, 0, 1, 0, 0, 0, 2, 0, 0, 0, 0, 0, -12, 0, 4, 0, 0, 0, 12, 0, 12, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, -10, 0, 6, 0, 0, 0, -4, 0, -12, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -6, 13], 'euler17': [1, 0, 0], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -8, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, 2, 37], 'euler41': [1, -2, 41], 'euler43': [1, -8, 43], 'euler47': [1, -8, 47], 'euler5': [1, -2, 5], 'euler53': [1, -2, 53], 'euler59': [1, 12, 59], 'euler61': [1, -4, 61], 'euler67': [1, -12, 67], 'euler7': [1, -1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 8, 73], 'euler79': [1, -8, 79], 'euler83': [1, 0, 83], 'euler89': [1, 10, 89], 'euler97': [1, 12, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -2, 5], [1, -1, 0], [1, 0, 11], [1, -6, 13], [1, 0, 0], [1, 2, 19], [1, 0, 23], [1, -8, 29], [1, 0, 31], [1, 2, 37], [1, -2, 41], [1, -8, 43], [1, -8, 47], [1, -2, 53], [1, 12, 59], [1, -4, 61], [1, -12, 67], [1, 0, 71], [1, 8, 73], [1, -8, 79], [1, 0, 83], [1, 10, 89], [1, 12, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/72828/y'], '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': '2-72828-1.1-c1-0-13', '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': '2-72828-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 24.11502659838013, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2126746618887898698, 'z1': {'__RealLiteral__': 0, 'data': '0.7125986581304658', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2126746618887898698', 'Lhash_array': ['2126746618887898698'], 'factors': ['2-72828-1.1-c1-0-13'], 'label': '2-72828-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/72828/y'}