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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '976220985929437224', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 154.27097670511378, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1, -1]], [7, [1, -1]], [23, [1, 1]]], 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '19320.1', 'coefficient_field': '1.1.1.1', 'conductor': 19320, 'conductor_radical': 4830, 'degree': 2, 'euler_factors': [[1], [1, -1], [1, -1], [1, -1], [1, 4, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1], [1, 2, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, 12, 59], [1, -14, 61], [1, 12, 67], [1, -16, 71], [1, 14, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 26, 'label': '2-19320-1.1-c1-0-26', 'leading_term': '6.51253705439', '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/19320/ba', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.554341350684685, 2.641365558459372, 2.777559581762984, 1.750339100356916, -0.01672559899270824, -1.514376865143516, -1.8020803913931, -0.8327398891459585, 0.3616746823800103, 0.5332745072516091, -0.4990955404622686, -1.465267696156569, -0.8312907695863849, 1.435199464779918, 3.478839573787399, 3.327148549661437, 1.131732160291693, -0.7587202159162288, -0.3528593512895085, 1.576044546919505, 2.286885775183676, 0.4647811798086785, -1.887007428435828, -1.741832845617343, 1.02869460328652, 3.176406308811737, 2.024284959392343, -1.089747784211167, -2.515487466112793, -1.025025143913924, 0.8150098344623365, 0.5098702953223312, -0.8092324387137954, -0.3393863401193164, 1.834685559213358, 2.567505403335209, 0.3877816087192888, -2.040489668569208, -1.794316086001368, -0.1230866036796259, -0.3548822656822791, -2.309600928627395, -2.266995397721802, 0.8713280278566362, 2.940991493889697, 0.3710951753744094, -4.035310666230485, -4.747985876378158, -1.493262143309864, 0.6741182124321689, -0.761313616763048, -2.441646884375557, -1.244829749212219, 0.6526478063533423, 0.01814175349628639, -1.626187780948761, -0.8236333329689308, 1.484942936568985, 1.559152243090132, -0.3261290530371306, -0.2820018838095484, 1.874795530841727, 1.727297041001475, -1.753564253762547, -3.411175664691511, -0.2264216223259936, 3.243551146261912, 2.273791008839421, -0.2268522588264497, 0.8635787943697439, 3.806132746746339, 3.320318074996615, 0.07926916676960974, -0.8219332548451517, 0.7275401371761033, 0.1127040103413485, -2.763499592258909, -2.878409484009331, 0.4857251386740214, 2.024865132229068, -0.1665484077211832, -1.585316546630011, -0.02073542084453831, 0.8943415992506641, -0.3703944682598542, -0.1347875272611092, 2.278892166260541, 1.954576576977083, -1.883260788545431, -2.586910120042515, 2.455750845311667, 6.223083322445167, 3.73192549872564, 0.1385884438897156, 0.6507647603071737, 1.569918092352949, -1.225803475069534, -3.77311657517214, -1.900024913909795, 0.7342190067996537, 0.1740614965556621, -0.4608865328338391, 1.634666867763048, 2.707123413319457, 0.3843007169477688, -1.111540942640803, 0.1361963196724416, -0.5442265234248659, -4.136351394277856, -4.325315260588025, 0.3689617589060436, 2.693771342088605, 0.0642819197700077, -0.8419440327007269, 2.329353932374362, 2.997299099728906, -0.8510126157554964, -2.52142410998184, 0.0718117732889362, 1.016254243922578], 'positive_zeros': ['1.247710192829133', '2.161010215303590', '2.650532265030181', '3.355390404173569', '4.372110345104147', '4.801542132477957', '5.543287624117810', '6.168581531091734', '6.911683528648977', '7.616046270553266', '8.088428359183361', '8.545329000082698', '9.282486716067283', '10.03134311309943', '10.17748868855932', '10.93976434011239', '11.52038537280413', '12.37114149870741', '12.66546156213351', '13.38854999145867', '13.75250434876020', '14.33575448755656', '14.95185587735242', '15.28861433154526', '15.88582962243242', '16.51254284587584', '17.21132534604852', '17.41145918315046', '18.25729050517799', '18.63458478513659', '19.01141976392497', '19.71563898641206'], 'prelabel': '2-19320-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.420586810014806, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 976220985929437224, 'z1': {'__RealLiteral__': 0, 'data': '1.247710192829133', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.161010215303590', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.650532265030181', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 154.27097670511378, 'bad_primes': [2, 3, 5, 7, 23], 'central_character': '1.1', 'conductor': 19320, 'conductor_radical': 4830, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -4, 0, -2, 0, 1, 0, 2, 0, -4, 0, 1, 0, -1, 0, 1, 0, 1, 0, -2, 0, 8, 0, -4, 0, 1, 0, 6, 0, -2, 0, -6, 0, -4, 0, 1, 0, 8, 0, 1, 0, 2, 0, -10, 0, -4, 0, -4, 0, -12, 0, 14, 0, 1, 0, -2, 0, -12, 0, -1, 0, 16, 0, -14, 0, 1, 0, -4, 0, 8, 0, 1, 0, -12, 0, 2, 0, -2, 0, -14, 0, -2, 0, 8, 0, -4, 0, 2, 0, -4, 0], 'euler11': [1, 4, 11], 'euler13': [1, 2, 13], 'euler17': [1, -2, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 1, 0], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, -8, 31], 'euler37': [1, -6, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, -1, 0], 'euler53': [1, 10, 53], 'euler59': [1, 12, 59], 'euler61': [1, -14, 61], 'euler67': [1, 12, 67], 'euler7': [1, -1, 0], 'euler71': [1, -16, 71], 'euler73': [1, 14, 73], 'euler79': [1, -8, 79], 'euler83': [1, 12, 83], 'euler89': [1, 14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, -1, 0], [1, -1, 0], [1, 4, 11], [1, 2, 13], [1, -2, 17], [1, 4, 19], [1, 1, 0], [1, 2, 29], [1, -8, 31], [1, -6, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, 10, 53], [1, 12, 59], [1, -14, 61], [1, 12, 67], [1, -16, 71], [1, 14, 73], [1, -8, 79], [1, 12, 83], [1, 14, 89], [1, -2, 97]], 'index': 26, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/19320/ba'], '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': '2-19320-1.1-c1-0-26', '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': '2-19320-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.420586810014806, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 976220985929437224, 'z1': {'__RealLiteral__': 0, 'data': '1.247710192829133', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '976220985929437224', 'Lhash_array': ['976220985929437224'], 'label': '2-19320-1.1-c1-0-26', 'type': 'ECQ', 'url': 'EllipticCurve/Q/19320/ba'}