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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 4, 'A8': 0, 'A9': 0, 'Lhash': '1953414658785278145', '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': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 390.94756829618893, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, 1]], [17, [1, 1]]], 'bad_primes': [2, 3, 5, 17], 'central_character': '48960.1', 'coefficient_field': '1.1.1.1', 'conductor': 48960, 'conductor_radical': 510, 'degree': 2, 'euler_factors': [[1], [1], [1, 1], [1, -4, 7], [1, -4, 11], [1, -2, 13], [1, 1], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, -6, 37], [1, 2, 41], [1, 12, 43], [1, -8, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, 14, 73], [1, -12, 79], [1, -4, 83], [1, 10, 89], [1, -18, 97]], 'gamma_factors': [[], [0]], 'index': 143, 'label': '2-48960-1.1-c1-0-143', 'leading_term': '7.21870793079', '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/48960/de', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.682691779701721, 2.646819315413841, 2.371966826759835, 1.014562516055998, -0.3787905323159166, -0.580918823013487, 0.5375994216522184, 1.529453637406158, 0.6484714336038351, -2.077628842257208, -4.359322307791204, -3.836578812247648, -0.8303244708998662, 1.746670261234148, 1.670751106176975, 0.003092922200300778, -0.5133396856471223, 0.6543643772740813, 1.063677841234647, -0.9309286975751411, -3.190756583679438, -2.430122212559816, 0.8390384305738854, 2.534210040107472, 0.7503670695671028, -1.316571157254094, -0.07756884420320966, 2.937760475376165, 3.372269134134248, 0.7735749096079106, -0.8704832840129251, 0.3642459998055357, 1.54319430176463, 0.3958468445285103, -0.5390109298528069, 1.257304042558261, 2.83012603852559, 0.110794602957845, -4.499741287978017, -4.861920308475822, -0.674039919079301, 2.048868548848281, 0.6048587359982492, -0.9543430259313619, 0.2033659026707112, 1.169060902565984, -0.08621475435788203, -0.391888277338911, 1.856960695822548, 2.190373122944322, -2.042098638764132, -5.473253608761321, -3.071194269936372, 1.081693741233369, 0.8108428271127353, -1.828637059198402, -1.458544485361852, 0.6255627142927825, 0.2766018976138062, -0.661680625964115, 1.250642265788085, 2.719645271055815, -0.3944862654655355, -3.874695131483423, -1.977218092974852, 1.856378634076598, 1.488942076881924, -0.6194495658684526, 0.7152779574757128, 2.781307365829642, 1.117518998085229, -0.8781945022404762, 0.8005537519923952, 1.986136986188758, -0.8812867203497265, -2.481751178891786, 1.001834446442227, 3.697797948574337, 1.334127365752525, -0.9502386674748329, 0.06582303842475065, -0.418804677568865, -3.58317888802746, -3.456568814878265, 0.3334498996099845, 1.282689234356301, -0.4601295997658557, 0.8892593129220829, 3.077571918433907, -0.1723453517797763, -4.983811682098875, -3.801951479844904, 0.1425962326702745, 0.3454606279857028, -0.2905955493538174, 1.981764851029075, 2.762293867476853, 0.2230526688143205, 0.1271305767322779, 2.804533235610575, 2.080800367446495, -0.03595275175445428, 3.411597337446145, 8.165140922519415, 5.643274408175961, -0.0130616983638878, -0.5898782472104633, 0.8010673191338878, -0.8736185337675547, -1.880473652594155, -0.3030687637596391, -0.3688641879496957, -0.5109476161303965, 3.741157837091105, 6.328901565735201, 0.5752589409174873, -5.47338106136973, -3.252455686594872, 0.638441627251699, -0.5866262432820675], 'positive_zeros': ['1.167321214397388', '1.650854889795661', '2.320515648144411', '3.313805501071233', '4.000523145464574', '4.380266822751130', '4.910741739323524', '5.687780398067160', '6.318901393929916', '6.756751442774723', '7.573938889784973', '7.951734532291308', '8.559022073015689', '8.865549622449343', '9.505869862208261', '10.28866912758262', '10.81436722770020', '11.22178827847548', '11.73604282081450', '12.05942138234862', '12.64988283361120', '13.41661358677385', '13.82242336103356', '14.40826320431038', '14.79558098155377', '15.12801371301830', '15.72855198162192', '16.36287569795695', '16.89813027333787', '17.18023870914923', '17.84867153005972', '18.17186425213209', '18.68957231927725', '19.19488386400210', '19.85176573526204'], 'prelabel': '2-48960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.77239409621882, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1953414658785278145, 'z1': {'__RealLiteral__': 0, 'data': '1.167321214397388', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.650854889795661', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.320515648144411', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 390.94756829618893, 'bad_primes': [2, 3, 5, 17], 'central_character': '1.1', 'conductor': 48960, 'conductor_radical': 510, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, -1, 0, 4, 0, 0, 0, 4, 0, 2, 0, 0, 0, -1, 0, -4, 0, 0, 0, -4, 0, 1, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, 6, 0, 0, 0, -2, 0, -12, 0, 0, 0, 8, 0, 9, 0, 0, 0, -2, 0, -4, 0, 0, 0, -12, 0, -2, 0, 0, 0, -2, 0, 4, 0, 0, 0, -4, 0, -14, 0, 0, 0, 16, 0, 12, 0, 0, 0, 4, 0, 1, 0, 0, 0, -10, 0, 8, 0, 0, 0, 4, 0, 18, 0, 0, 0], 'euler11': [1, -4, 11], 'euler13': [1, -2, 13], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 4, 31], 'euler37': [1, -6, 37], 'euler41': [1, 2, 41], 'euler43': [1, 12, 43], 'euler47': [1, -8, 47], 'euler5': [1, 1, 0], 'euler53': [1, 2, 53], 'euler59': [1, 12, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, 4, 71], 'euler73': [1, 14, 73], 'euler79': [1, -12, 79], 'euler83': [1, -4, 83], 'euler89': [1, 10, 89], 'euler97': [1, -18, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 1, 0], [1, -4, 7], [1, -4, 11], [1, -2, 13], [1, 1, 0], [1, 4, 19], [1, 4, 23], [1, -2, 29], [1, 4, 31], [1, -6, 37], [1, 2, 41], [1, 12, 43], [1, -8, 47], [1, 2, 53], [1, 12, 59], [1, 2, 61], [1, -4, 67], [1, 4, 71], [1, 14, 73], [1, -12, 79], [1, -4, 83], [1, 10, 89], [1, -18, 97]], 'index': 143, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/48960/de'], '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': '2-48960-1.1-c1-0-143', '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': '2-48960-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.77239409621882, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1953414658785278145, 'z1': {'__RealLiteral__': 0, 'data': '1.167321214397388', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1953414658785278145', 'Lhash_array': ['1953414658785278145'], 'label': '2-48960-1.1-c1-0-143', 'type': 'ECQ', 'url': 'EllipticCurve/Q/48960/de'}