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lfunc_lfunctions • Show schema
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{'A10': -3, 'A2': -1, 'A3': 0, 'A4': 1, 'A5': 3, 'A6': 0, 'A7': 0, 'A8': -1, 'A9': 0, 'Lhash': '1279421715498854723', 'a10': [-0.9486832980505138, 0], 'a2': [-0.7071067811865475, 0], 'a3': [0.0, 0], 'a4': [0.5, 0], 'a5': [1.3416407864998738, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 161.98452554036948, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1]], [7, [1]], [23, [1, 1]]], 'bad_primes': [2, 3, 7, 23], 'central_character': '20286.1', 'coefficient_field': '1.1.1.1', 'conductor': 20286, 'conductor_radical': 966, 'degree': 2, 'euler_factors': [[1, 1], [1], [1, -3, 5], [1], [1, 4, 11], [1, -3, 13], [1, 4, 17], [1, 0, 19], [1, 1], [1, 3, 29], [1, -6, 31], [1, 9, 37], [1, -9, 41], [1, 3, 43], [1, 7, 47], [1, -4, 53], [1, -6, 59], [1, 10, 61], [1, -4, 67], [1, -6, 71], [1, -8, 73], [1, -8, 79], [1, -4, 83], [1, 14, 89], [1, -7, 97]], 'gamma_factors': [[], [0]], 'index': 48, 'label': '2-20286-1.1-c1-0-48', 'leading_term': '4.52666481254', '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/20286/bb', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.067855830774879, 1.742817861838023, 1.664635211687269, 0.7599290824338479, -0.5038588549117063, -1.280124058294147, -0.9993125041674842, -0.01336480837376039, 0.525281825265309, -0.2561374807081065, -1.793625615995852, -2.214625432977707, -0.1052031981541183, 3.598744599730022, 5.816622249749983, 4.049747394063167, -0.8438652804744808, -4.999028709157295, -5.190106824498009, -2.091592621961336, 0.5856992315216484, 0.2976640879936765, -1.659127778371201, -2.218945604368601, -0.693546229257677, 0.4341921786592777, -0.8512297258154287, -3.013293886359042, -2.870690321236762, -0.04476150465840586, 2.31289250540745, 1.738452782834308, -0.2637631037644375, -0.5737646332015757, 1.029458468190423, 1.855331561376529, 0.6393186282946035, -0.5761405943784886, 0.09459880315902167, 1.271093262683224, 0.7343926820566884, -0.6425778765766481, -0.3677777954536327, 0.888375126492809, -0.3323284411054534, -4.250189598244391, -5.985001497537971, -2.30712553525588, 2.784928600142361, 3.143818223317777, -0.7480885089627481, -2.909854673904947, -1.217364618338625, 0.03059757002030695, -1.731117405923926, -2.488997958253203, 1.271047265728283, 5.481636027280784, 4.114689110674201, -1.149543721774873, -3.354387117100948, -1.011721831439237, 0.5038847094364277, -1.425934628018079, -2.752869783488952, -0.5661922939087605, 1.761847891355204, 0.7866234851389158, -1.221419457271281, -0.9640668848385768, 0.20079270404107, -0.1091986546912955, -0.376712497173257, 1.073969850239543, 1.593195826019748, -0.9578500574152481, -2.898545897671578, -0.5067887627775394, 2.682687756500944, 1.340880041184998, -2.388585245322155, -2.784481707562361, -0.4874354158048255, -0.08261775533575436, -0.7576978095655882, 1.171006855779318, 3.027980771765955, -0.361569229085473, -5.544302032512454, -4.716610708703301, 0.06752111460832907, -0.5143020172081909, -6.460370167655886, -7.828725743123475, -1.908757174596629, 2.612598167981775, 1.136238819422319, -0.5126769071629792, 1.400788245459412, 2.373529316035919, -0.09062557554701069, -1.733880554659183, -0.5696932070227345, -0.006180805895878685, -0.6874744196572251, 0.3733919150237658, 1.659346403732503, -1.108287474775807, -5.337714533796032, -4.680374409211719, -0.4929286705622659, 0.8490381243276829, -0.4668471422608076, 0.1284596830699076, 1.681998590796488, 0.8983857701100332, 0.02213302014137736, 1.361345802661071, 1.077247598790634, -2.196786424843561], 'positive_zeros': ['1.148663405317282', '2.003426418152265', '2.450812715168408', '3.257906533092283', '4.210264582657301', '5.169973208802493', '5.542062547063662', '6.353623841616030', '6.639812128064931', '7.503457153982083', '8.210997821878132', '8.605619995061618', '9.348219294207286', '9.732715398116441', '10.37037725012787', '10.81586660082728', '11.22103557785677', '12.10134207825107', '12.70511613260107', '13.42884429511091', '13.51423391389153', '14.18713553571539', '14.94369937618846', '15.59866799490326', '15.85246959404697', '16.54510554461672', '17.08384637502635', '17.68509005484450', '17.96583047564200', '18.34005148263593', '18.92558653158722', '19.53185861338059'], 'prelabel': '2-20286-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.727314152654891, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1279421715498854723, 'z1': {'__RealLiteral__': 0, 'data': '1.148663405317282', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '2.003426418152265', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.450812715168408', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 161.98452554036948, 'bad_primes': [2, 3, 7, 23], 'central_character': '1.1', 'conductor': 20286, 'conductor_radical': 966, 'degree': 2, 'dirichlet_coefficients': [1, -1, 0, 1, 3, 0, 0, -1, 0, -3, -4, 0, 3, 0, 0, 1, -4, 0, 0, 3, 0, 4, -1, 0, 4, -3, 0, 0, -3, 0, 6, -1, 0, 4, 0, 0, -9, 0, 0, -3, 9, 0, -3, -4, 0, 1, -7, 0, 0, -4, 0, 3, 4, 0, -12, 0, 0, 3, 6, 0, -10, -6, 0, 1, 9, 0, 4, -4, 0, 0, 6, 0, 8, 9, 0, 0, 0, 0, 8, 3, 0, -9, 4, 0, -12, 3, 0, 4, -14, 0, 0, -1, 0, 7, 0, 0, 7, 0, 0, 4], 'euler11': [1, 4, 11], 'euler13': [1, -3, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, 1, 0], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, -6, 31], 'euler37': [1, 9, 37], 'euler41': [1, -9, 41], 'euler43': [1, 3, 43], 'euler47': [1, 7, 47], 'euler5': [1, -3, 5], 'euler53': [1, -4, 53], 'euler59': [1, -6, 59], 'euler61': [1, 10, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 0], 'euler71': [1, -6, 71], 'euler73': [1, -8, 73], 'euler79': [1, -8, 79], 'euler83': [1, -4, 83], 'euler89': [1, 14, 89], 'euler97': [1, -7, 97], 'euler_factors': [[1, 1, 0], [1, 0, 0], [1, -3, 5], [1, 0, 0], [1, 4, 11], [1, -3, 13], [1, 4, 17], [1, 0, 19], [1, 1, 0], [1, 3, 29], [1, -6, 31], [1, 9, 37], [1, -9, 41], [1, 3, 43], [1, 7, 47], [1, -4, 53], [1, -6, 59], [1, 10, 61], [1, -4, 67], [1, -6, 71], [1, -8, 73], [1, -8, 79], [1, -4, 83], [1, 14, 89], [1, -7, 97]], 'index': 48, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/20286/bb'], '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': '2-20286-1.1-c1-0-48', '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': '2-20286-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 12.727314152654891, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1279421715498854723, 'z1': {'__RealLiteral__': 0, 'data': '1.148663405317282', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1279421715498854723', 'Lhash_array': ['1279421715498854723'], 'label': '2-20286-1.1-c1-0-48', 'type': 'ECQ', 'url': 'EllipticCurve/Q/20286/bb'}