-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 1, 'Lhash': '515276804400837108', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, 1]], [13, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '212160.1', 'coefficient_field': '1.1.1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, 1], [1, 0, 7], [1, 0, 11], [1, 1], [1, 1], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 0, 59], [1, -2, 61], [1, -12, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, -6, 97]], 'gamma_factors': [[], [0]], 'index': 117, 'label': '2-212160-1.1-c1-0-117', 'leading_term': '8.40845815362', '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/212160/et', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.83350307455359, 2.222749538156195, 0.6798907872525563, -1.513632773734851, -2.058335682128364, -0.1112222516753617, 2.302957983543238, 2.446880956313453, 0.4495115475657566, -0.7359209970635733, 0.4107085155948377, 1.574632438400811, 0.2113327816774125, -2.113456859918835, -2.028769598004393, -0.09157834715950737, -0.0615218760761323, -2.21283351091563, -2.468933247415066, 0.008969065005409248, 0.134217837268098, -4.490778762058357, -8.084199937826094, -5.383659719200201, -0.4125602668837743, 0.4777836515646658, -0.8092195789746187, 1.065185817986251, 4.235814537147306, 3.481428741208337, 0.5059194865085168, 0.2701691591517232, 1.331771171798525, -0.009609601480518606, -1.140502051426201, 1.033018753035661, 2.282571953156106, -0.7165486462263649, -2.752183551791071, -0.4338065467732391, 0.53494588680595, -2.48468707104469, -2.928467884818226, 0.9261773142193493, 1.474695107232785, -2.395321675879169, -2.705218576753967, 0.847523052534346, 0.6746626720724928, -2.226802915528228, -1.295898730657157, 0.5370899141241307, -2.145111656760228, -4.35715816417087, -1.56007028329649, 0.386540152912467, -1.330340514361148, -0.8480173030973432, 1.850480988620699, 0.9717272134694233, -0.9906019449701658, 0.7410840008756941, 1.719280835149508, -0.1694178189069266, 1.638866815233917, 5.841170149180352, 3.607922809479943, -1.425079132589216, -0.08258084525110977, 2.383608854089294, -0.7186189392345166, -1.677530265774749, 3.217930439671253, 4.375053175916758, 0.2629274439853441, -0.5376102771954495, 1.034844385161121, -0.1737431568434084, -0.4893576574114727, 0.8452045544315181, -1.716916104648617, -4.620078035878921, -1.898760620531845, 0.4736845384524351, -0.8682497931316229, 0.6496329142029029, 2.581355002944939, -2.291251317851065, -6.184574833488745, -1.995177372305193, 0.9009030968972656, -0.8686522759004603, 1.295144856346904, 4.412792966453976, 0.9454133451017132, -1.837887017398569, 0.734007958855888, 0.7813328743976001, -0.9966627890059028, 1.582961134214204, 2.544928101552241, -1.157329390129138, -1.225542508430929, 1.259917879059202, -0.4039017341286636, -1.134043195204483, 1.338446097307173, 0.03722355891820732, -1.907927071997692, 0.9241522497222672, 1.231664894567203, -1.465721996866935, 1.381176933137829, 3.406860301317824, -2.3456596608432, -4.260134400933919, 0.7306046562341094, 0.4385420510948173, -2.634340215584187, -0.08707420904406615], 'positive_zeros': ['0.8236225211633329', '1.510226836106998', '2.306326634064683', '2.690257888742556', '3.271081200068474', '4.015670240024106', '4.239676065023777', '4.999033085883636', '5.262279219029397', '6.283086609021919', '6.578276808582860', '6.914716776121687', '7.842836988115013', '7.928923910063482', '8.498882491128115', '8.909499849421934', '9.453410780250979', '10.03941947926250', '10.31174399127694', '10.94076759907165', '11.35306108350644', '11.93407154874616', '12.30490312833773', '12.87178373824575', '13.09548561964561', '13.87779031264927', '14.08346665345333', '14.57302331297426', '15.08939218966368', '15.42869496350595', '15.96894730973264', '16.12714362060282', '16.90646262807116', '17.25528608689018', '17.70624349209407', '18.10048531896731', '18.76955317002841', '19.07058605154410', '19.47611888466324', '19.82433055340965'], 'prelabel': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 515276804400837108, 'z1': {'__RealLiteral__': 0, 'data': '0.8236225211633329', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.510226836106998', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.306326634064683', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1694.1061292834854, 'bad_primes': [2, 3, 5, 13, 17], 'central_character': '1.1', 'conductor': 212160, 'conductor_radical': 6630, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, -4, 0, 0, 0, 0, 0, 1, 0, 1, 0, 6, 0, 8, 0, 0, 0, 0, 0, -6, 0, -1, 0, 10, 0, -4, 0, -1, 0, -4, 0, -7, 0, -1, 0, 2, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 1, 0, 12, 0, 0, 0, 0, 0, 14, 0, 1, 0, 0, 0, -8, 0, 1, 0, 4, 0, 1, 0, 6, 0, -6, 0, 0, 0, 8, 0, 4, 0, 6, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -6, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, 6, 37], 'euler41': [1, -10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 1, 0], 'euler53': [1, -2, 53], 'euler59': [1, 0, 59], 'euler61': [1, -2, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, 0, 71], 'euler73': [1, -14, 73], 'euler79': [1, 8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 6, 89], 'euler97': [1, -6, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 1, 0], [1, 0, 7], [1, 0, 11], [1, 1, 0], [1, 1, 0], [1, 4, 19], [1, 0, 23], [1, -6, 29], [1, -8, 31], [1, 6, 37], [1, -10, 41], [1, 4, 43], [1, 4, 47], [1, -2, 53], [1, 0, 59], [1, -2, 61], [1, -12, 67], [1, 0, 71], [1, -14, 73], [1, 8, 79], [1, -4, 83], [1, 6, 89], [1, -6, 97]], 'index': 117, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/212160/et'], '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': '2-212160-1.1-c1-0-117', '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': '2-212160-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 41.159520518143616, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 515276804400837108, 'z1': {'__RealLiteral__': 0, 'data': '0.8236225211633329', 'prec': 60}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '515276804400837108', 'Lhash_array': ['515276804400837108'], 'label': '2-212160-1.1-c1-0-117', 'type': 'ECQ', 'url': 'EllipticCurve/Q/212160/et'}