-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': -2, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': -4, 'A8': 0, 'A9': 1, 'Lhash': '1526928697996642619', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [-1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 540.683042166494, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [23, [1]]], 'bad_primes': [2, 23], 'central_character': '67712.1', 'coefficient_field': '1.1.1.1', 'conductor': 67712, 'conductor_radical': 46, 'degree': 2, 'euler_factors': [[1], [1, 2, 3], [1, 2, 5], [1, 4, 7], [1, 2, 11], [1, -2, 13], [1, -2, 17], [1, -2, 19], [1], [1, 6, 29], [1, 0, 31], [1, 10, 37], [1, 6, 41], [1, -6, 43], [1, -8, 47], [1, -6, 53], [1, 14, 59], [1, 2, 61], [1, -10, 67], [1, 12, 71], [1, -14, 73], [1, 8, 79], [1, 6, 83], [1, -2, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 6, 'label': '2-67712-1.1-c1-0-6', 'leading_term': '1.88218529765', '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/67712/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.3545941320991735, 0.08638338708624282, -0.9905995426551023, -2.159318293580064, -1.968478225368381, 0.510648991888, 4.255446800807643, 6.495498727962823, 5.103028919969747, 1.039507494102704, -2.176361186983438, -2.064657303369992, 0.08619124088960013, 0.9540473618132769, -0.4470347123189562, -1.477790984934243, 0.3007829019303658, 3.347902434273629, 4.014077954161454, 1.67730874500556, -0.4045701050352541, 0.04355264565386192, 1.158623329931836, 0.4349087953096556, -0.9103024163583953, -0.1351949940539276, 1.889256844159152, 1.815343491616284, -0.1008577694553874, 0.1944829276482702, 3.35164250868858, 4.302293759988326, 0.279157818972666, -3.635866979537846, -1.915311431891902, 2.358742540015771, 2.266196623966117, -1.77029655251923, -3.145246995864737, -0.284815304531562, 1.539590379176073, 0.05442096471556587, -0.7574962974426014, 1.001038577791214, 1.733855306272369, -0.115933119496373, -1.007174651049527, 0.4038546137816631, 0.8079680421229258, -0.3005187407488539, 0.7453231844164169, 3.278910894038329, 2.136518447396302, -1.527253330600214, -0.49821914531517, 4.430560391899129, 3.436542030957181, -5.182365744242386, -10.45416127205545, -6.423080287311418, -0.6705230727182717, 0.145579084533029, -0.4999354686159397, 0.6882928575949099, 0.8222979213182001, -0.6436007336619789, -0.1564055434950507, 1.126139764246265, -0.759882063075335, -2.78295124105415, 0.1131583449938603, 3.928969905341275, 2.601502232092795, -0.3254389874859712, 0.2347199135628487, 0.5479880094477909, -2.281191017661938, -2.60216390322266, 1.287284817617196, 2.035369328540137, -1.128451772498737, 0.3730982853580071, 6.000488291817649, 5.339195497469007, -1.219596239641908, -2.682486680479425, 1.671295868471097, 2.866589495900549, 0.2544028578221224, -0.334071825585573, 0.4562752611620869, -0.1100329240899192, 0.170855596490541, 1.210389007518684, -0.1171910502988198, -0.6081966804674958, 3.1440623213348, 3.962295446744657, -2.634563562485737, -6.261328328739141, -0.509308317647702, 4.149652608710335, 1.303512660451752, -0.7320931878641658, 0.685461223246245, -2.029724418193615, -6.894526680312381, -5.01668117508616, 0.1012153776492465, 0.2514731497266013, -1.086928490728541, 0.7810597381656985, 1.519660910124264, -0.2012221612506708, -0.003817856592638851, 0.5198922284486798, -1.446652140897305, -1.538776438321711, 0.2732658151913736, -2.699017266847185], 'positive_zeros': ['0.5285705204077028', '1.461990157237688', '2.563063740723578', '3.239410648196120', '3.688928433417742', '4.224341675243469', '5.172030471926290', '5.491866799759207', '6.066992892099055', '6.516993145621589', '7.233707865503066', '7.476338581565131', '8.263227272964122', '8.853736503442573', '9.394478430462438', '10.02183017439700', '10.50693315556252', '10.88037172691711', '11.48624405392854', '11.93807819610073', '12.41896669104856', '12.66182810591663', '13.38484119993041', '13.77746573532842', '14.36232490959404', '15.31224727008093', '15.53471310748769', '15.88071660704075', '16.38415331562118', '16.77259129979577', '17.18634487645958', '17.74404410444228', '18.45310765377435', '18.71247018639805', '19.06431086183788', '19.67079768414233'], 'prelabel': '2-67712-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.252592160154833, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1526928697996642619, 'z1': {'__RealLiteral__': 0, 'data': '0.5285705204077028', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.461990157237688', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.563063740723578', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 540.683042166494, 'bad_primes': [2, 23], 'central_character': '1.1', 'conductor': 67712, 'conductor_radical': 46, 'degree': 2, 'dirichlet_coefficients': [1, 0, -2, 0, -2, 0, -4, 0, 1, 0, -2, 0, 2, 0, 4, 0, 2, 0, 2, 0, 8, 0, 0, 0, -1, 0, 4, 0, -6, 0, 0, 0, 4, 0, 8, 0, -10, 0, -4, 0, -6, 0, 6, 0, -2, 0, 8, 0, 9, 0, -4, 0, 6, 0, 4, 0, -4, 0, -14, 0, -2, 0, -4, 0, -4, 0, 10, 0, 0, 0, -12, 0, 14, 0, 2, 0, 8, 0, -8, 0, -11, 0, -6, 0, -4, 0, 12, 0, 2, 0, -8, 0, 0, 0, -4, 0, 2, 0, -2, 0], 'euler11': [1, 2, 11], 'euler13': [1, -2, 13], 'euler17': [1, -2, 17], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 0], 'euler29': [1, 6, 29], 'euler3': [1, 2, 3], 'euler31': [1, 0, 31], 'euler37': [1, 10, 37], 'euler41': [1, 6, 41], 'euler43': [1, -6, 43], 'euler47': [1, -8, 47], 'euler5': [1, 2, 5], 'euler53': [1, -6, 53], 'euler59': [1, 14, 59], 'euler61': [1, 2, 61], 'euler67': [1, -10, 67], 'euler7': [1, 4, 7], 'euler71': [1, 12, 71], 'euler73': [1, -14, 73], 'euler79': [1, 8, 79], 'euler83': [1, 6, 83], 'euler89': [1, -2, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 2, 3], [1, 2, 5], [1, 4, 7], [1, 2, 11], [1, -2, 13], [1, -2, 17], [1, -2, 19], [1, 0, 0], [1, 6, 29], [1, 0, 31], [1, 10, 37], [1, 6, 41], [1, -6, 43], [1, -8, 47], [1, -6, 53], [1, 14, 59], [1, 2, 61], [1, -10, 67], [1, 12, 71], [1, -14, 73], [1, 8, 79], [1, 6, 83], [1, -2, 89], [1, -2, 97]], 'index': 6, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/67712/b'], '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': '2-67712-1.1-c1-0-6', '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': '2-67712-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 23.252592160154833, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1526928697996642619, 'z1': {'__RealLiteral__': 0, 'data': '0.5285705204077028', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1526928697996642619', 'Lhash_array': ['1526928697996642619'], 'factors': ['2-67712-1.1-c1-0-6'], 'label': '2-67712-1.1-c1-0-6', 'type': 'ECQ', 'url': 'EllipticCurve/Q/67712/b'}