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lfunc_lfunctions • Show schema
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{'A10': 8, 'A2': -2, 'A3': 0, 'A4': 2, 'A5': -4, 'A6': 0, 'A7': -3, 'A8': 0, 'A9': 0, 'Lhash': '31374660670746329', 'a10': [2.5298221281347035, 0], 'a2': [-1.414213562373095, 0], 'a3': [0.0, 0], 'a4': [1.0, 0], 'a5': [-1.7888543819998317, 0], 'a6': [0.0, 0], 'a7': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 206.4691845064248, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [13, [1]], [17, [1, 1]]], 'bad_primes': [3, 13, 17], 'central_character': '25857.1', 'coefficient_field': '1.1.1.1', 'conductor': 25857, 'conductor_radical': 663, 'degree': 2, 'euler_factors': [[1, 2, 2], [1], [1, 4, 5], [1, 3, 7], [1, 4, 11], [1], [1, 1], [1, 4, 19], [1, 6, 23], [1, -2, 29], [1, -7, 31], [1, 2, 37], [1, 2, 41], [1, -11, 43], [1, 2, 47], [1, 2, 53], [1, -14, 59], [1, -5, 61], [1, 13, 67], [1, 12, 71], [1, -7, 73], [1, -1, 79], [1, -4, 83], [1, 12, 89], [1, -3, 97]], 'gamma_factors': [[], [0]], 'index': 13, 'label': '2-25857-1.1-c1-0-13', 'leading_term': '2.78531188601', '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': 2, 'origin': 'EllipticCurve/Q/25857/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, -0.1635070076869027, -0.52114969633861, -0.6705413275392575, -0.0883737595300372, 1.421203696683826, 3.270115234627426, 4.210042032964559, 3.276623904579767, 0.9022016966209769, -1.025640272560987, -0.6921685279502007, 1.703474522183167, 3.74018506937093, 3.080569173249932, 0.2024733541034945, -1.699157612531678, -0.2261913815533186, 2.92704345305119, 3.170777743432863, -1.799488145826669, -8.582653978298422, -11.0112057662831, -6.750897326234069, 0.04552551466171767, 3.380718056906851, 1.858172247297124, -0.7611343314318172, -0.9609995427148899, 0.5716737306223358, 1.140724831927058, 0.3042621560436914, -0.12173969034342, 0.467139553425158, 0.559445626598974, -0.4562206419979835, -0.782856384826601, 0.8297769706218502, 2.551600259584896, 2.059561702704945, 0.3088639957179414, -0.0156547918541373, 0.9209185097569195, 0.4356625199446145, -1.59650294215597, -1.904861282405508, 0.4592168887929551, 1.623513381152555, -0.873327537841724, -3.136465201230935, -0.9275846399270441, 2.348968558246302, 0.313699845704811, -4.871939106933175, -3.831880538385619, 5.304549373764461, 11.73442521123551, 6.528155075511854, -4.360771307160827, -8.623854739562345, -4.285901619381161, 0.3671853129822914, 0.5608255184284556, -0.4394816581369454, 0.06171271244522584, 0.1148397271832955, -0.8632743309505878, 0.06730588149304977, 3.084779773437644, 4.020430558242405, 1.614296236001463, -0.01189959718694265, 1.346351200472186, 2.482179573862009, 1.159626078444141, -0.2382582764910853, 0.009466919216905775, 0.1930523689462164, -0.1949691468816088, 0.5165866609661592, 1.167739129467295, -0.8771257764677178, -2.859668847137444, -0.3146378596083984, 2.15571519914422, -4.3497089988107, -16.11650182437393, -18.64102628924075, -8.712639832791442, 0.2646679581977207, -0.1131037047804372, -2.127233862949826, 1.06571468212205, 3.658958576114164, 0.9016064253617558, -1.050722424180174, 1.571129177981982, 1.652035749547813, -4.558038779506091, -8.640430479931798, -4.599444333906884, 0.8612923377878678, 0.8943707877336947, -1.09058016999311, -0.5680223849984432, 0.3143226584530104, -0.3932437174173224, -0.4561363727328272, 0.3366177696488634, -0.4268890423849503, -1.66343112177642, -0.8442697659835146, 0.2876068368910583, -0.083774997562281, 0.5355969691232227, 2.395411199201886, 1.333234423006042, -1.479466883820006, 0.2414463681289699, 4.170385915387699, 1.48611479839311], 'positive_zeros': ['1.019930560911377', '2.344313890450583', '2.837258618350146', '3.767051091659232', '4.268596105996029', '4.930949424890872', '5.998055435563203', '6.661078442904420', '7.159300982849877', '7.845606391720963', '8.077665886825475', '8.650660135538694', '9.149130879341451', '10.07045347006894', '10.25558060362490', '10.80906999544535', '11.45715804734053', '11.93521355466865', '12.55713851015045', '13.01545602576671', '13.61974823697928', '14.39559766271876', '15.21654880682016', '15.60688582258288', '15.97982786629228', '16.28280331170882', '16.74305801155062', '17.72667959147023', '17.76770916768760', '18.67616361800289', '18.99600253163678', '19.35565945530586', '19.62922848426083'], 'prelabel': '2-25857-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.369035615044762, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 31374660670746329, 'z1': {'__RealLiteral__': 0, 'data': '1.019930560911377', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.344313890450583', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.837258618350146', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 206.4691845064248, 'bad_primes': [3, 13, 17], 'central_character': '1.1', 'conductor': 25857, 'conductor_radical': 663, 'degree': 2, 'dirichlet_coefficients': [1, -2, 0, 2, -4, 0, -3, 0, 0, 8, -4, 0, 0, 6, 0, -4, -1, 0, -4, -8, 0, 8, -6, 0, 11, 0, 0, -6, 2, 0, 7, 8, 0, 2, 12, 0, -2, 8, 0, 0, -2, 0, 11, -8, 0, 12, -2, 0, 2, -22, 0, 0, -2, 0, 16, 0, 0, -4, 14, 0, 5, -14, 0, -8, 0, 0, -13, -2, 0, -24, -12, 0, 7, 4, 0, -8, 12, 0, 1, 16, 0, 4, 4, 0, 4, -22, 0, 0, -12, 0, 0, -12, 0, 4, 16, 0, 3, -4, 0, 22], 'euler11': [1, 4, 11], 'euler13': [1, 0, 0], 'euler17': [1, 1, 0], 'euler19': [1, 4, 19], 'euler2': [1, 2, 2], 'euler23': [1, 6, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, -7, 31], 'euler37': [1, 2, 37], 'euler41': [1, 2, 41], 'euler43': [1, -11, 43], 'euler47': [1, 2, 47], 'euler5': [1, 4, 5], 'euler53': [1, 2, 53], 'euler59': [1, -14, 59], 'euler61': [1, -5, 61], 'euler67': [1, 13, 67], 'euler7': [1, 3, 7], 'euler71': [1, 12, 71], 'euler73': [1, -7, 73], 'euler79': [1, -1, 79], 'euler83': [1, -4, 83], 'euler89': [1, 12, 89], 'euler97': [1, -3, 97], 'euler_factors': [[1, 2, 2], [1, 0, 0], [1, 4, 5], [1, 3, 7], [1, 4, 11], [1, 0, 0], [1, 1, 0], [1, 4, 19], [1, 6, 23], [1, -2, 29], [1, -7, 31], [1, 2, 37], [1, 2, 41], [1, -11, 43], [1, 2, 47], [1, 2, 53], [1, -14, 59], [1, -5, 61], [1, 13, 67], [1, 12, 71], [1, -7, 73], [1, -1, 79], [1, -4, 83], [1, 12, 89], [1, -3, 97]], 'index': 13, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/25857/a'], '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': '2-25857-1.1-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': 2, 'prelabel': '2-25857-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 14.369035615044762, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 31374660670746329, 'z1': {'__RealLiteral__': 0, 'data': '1.019930560911377', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '31374660670746329', 'Lhash_array': ['31374660670746329'], 'label': '2-25857-1.1-c1-0-13', 'type': 'ECQ', 'url': 'EllipticCurve/Q/25857/a'}