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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': 0, 'A8': 0, 'A9': -2, 'Lhash': '2139931915094694717', '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': [-0.6666666666666666, 0], 'algebraic': True, 'analytic_conductor': 86.0787333789403, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1, 1]], [7, [1]], [11, [1, 1]]], 'bad_primes': [2, 5, 7, 11], 'central_character': '10780.1', 'coefficient_field': '1.1.1.1', 'conductor': 10780, 'conductor_radical': 770, 'degree': 2, 'euler_factors': [[1], [1, 1, 3], [1, 1], [1], [1, 1], [1, -4, 13], [1, 6, 17], [1, 2, 19], [1, 9, 23], [1, -9, 29], [1, -4, 31], [1, -2, 37], [1, 3, 41], [1, -11, 43], [1, -12, 47], [1, 0, 53], [1, 0, 59], [1, -7, 61], [1, -5, 67], [1, 6, 71], [1, 2, 73], [1, 16, 79], [1, 9, 83], [1, 9, 89], [1, -4, 97]], 'gamma_factors': [[], [0]], 'index': 7, 'label': '2-10780-1.1-c1-0-7', 'leading_term': '3.11981209025', '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/10780/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.7285846370929044, 1.133367280903413, 0.8785780872507308, -0.1969547050280282, -1.806006337805477, -3.164023638779836, -3.37419650780413, -2.104916331281302, -0.05137389168216, 1.345176995425806, 0.9272392252854937, -1.137219245387054, -3.29432128724366, -3.819263660348478, -2.376135740409342, -0.4220595323208946, 0.1367868447982468, -1.129575233465685, -2.65634649629409, -2.492211171264153, -0.4479468395125941, 1.618488359761518, 1.869805014270891, 0.6307117005133343, -0.009848598429569831, 1.14614943914321, 2.68706078383756, 2.167480393884084, -0.6999918655020093, -3.272396100055644, -2.946847545857841, -0.3627868357438802, 1.368999335138761, 0.6942871847529328, -0.2928671019007902, 1.302963102922067, 4.945462156769319, 6.837071769331456, 4.64533735993518, 0.6275927116053254, -1.158590205011225, 0.09188630919711038, 1.426045105566798, 0.6372830688970349, -0.8043559701877465, -0.5042130090016975, 0.8531384603676523, 0.5698492050051976, -1.492049958484651, -2.174282570165489, 0.1882281664248596, 2.679319851591627, 1.700107393211575, -1.588503395720933, -2.770648530943946, -0.830983797515098, 0.1508319163453731, -2.75506432510499, -6.505418773726726, -6.271625896941057, -2.416108902546382, 0.3842081281021023, 0.2581067260919849, 0.2159955054530667, 2.301305444554321, 3.831760408560123, 2.017165453898301, -0.9574722675203321, -1.189137881443413, 0.6962156081948374, 0.94340016037188, -0.6426696243783213, -0.3824242504760674, 2.411470888120781, 3.42611974751762, 0.3725971794359736, -2.687536142082672, -1.603745172362423, 1.203789964892084, 1.079869825540529, -0.8531471932592402, 0.08631912211455192, 3.438573641549847, 3.783598055700483, -0.05619530704229629, -2.646674029973767, -0.7314626488805833, 1.810252759975998, 1.034335002849777, -0.6904854233873826, 0.2161755303653493, 1.953548608133039, 1.19162083487532, -0.5019567158095717, -0.07532735668647171, 0.4924994166919239, -2.198956291036821, -5.407659885223335, -3.802240741410136, 0.9141790876201673, 1.973536992949681, -1.27605843165511, -2.617636903546569, -0.09247516210961737, 1.002893865222935, -1.618622499159242, -2.873900265415094, 0.1493330777476439, 2.638922991947258, 0.7476955546354567, -1.785431642927376, -0.9673292098405443, 0.619911467198246, -0.05760345097506526, -0.4423169466274275, 1.499063152711113, 1.923979378944584, -1.583119916205896, -4.023189085021689, -1.271504585751517], 'positive_zeros': ['0.9646738707022310', '2.256504095732686', '2.878172435199233', '4.087379318388491', '4.301033127137961', '5.295808297087206', '6.176027443709012', '6.258146874829633', '7.196999701150778', '8.034754176834296', '8.629071153085343', '8.857317481326777', '10.04961982796493', '10.48791950692025', '11.09539850234481', '11.58898867727913', '12.07856306973311', '12.73525563828917', '13.37988290600961', '14.10812260169424', '14.28067856592035', '15.43884502959586', '15.86383408531792', '15.91994022999472', '16.90577569627787', '17.40714766965831', '17.89886741851528', '18.29332652328523', '19.02286787632758', '19.62973526609672'], 'prelabel': '2-10780-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.27786254365413, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2139931915094694717, 'z1': {'__RealLiteral__': 0, 'data': '0.9646738707022310', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '2.256504095732686', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.878172435199233', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 86.0787333789403, 'bad_primes': [2, 5, 7, 11], 'central_character': '1.1', 'conductor': 10780, 'conductor_radical': 770, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 0, 0, -2, 0, -1, 0, 4, 0, 1, 0, -6, 0, -2, 0, 0, 0, -9, 0, 1, 0, 5, 0, 9, 0, 4, 0, 1, 0, 0, 0, 2, 0, -4, 0, -3, 0, 11, 0, 2, 0, 12, 0, 0, 0, 6, 0, 0, 0, 1, 0, 2, 0, 0, 0, 7, 0, 0, 0, -4, 0, 5, 0, 9, 0, -6, 0, -2, 0, -1, 0, 0, 0, -16, 0, 1, 0, -9, 0, 6, 0, -9, 0, -9, 0, 0, 0, -4, 0, 2, 0, 4, 0, 2, 0], 'euler11': [1, 1, 0], 'euler13': [1, -4, 13], 'euler17': [1, 6, 17], 'euler19': [1, 2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 9, 23], 'euler29': [1, -9, 29], 'euler3': [1, 1, 3], 'euler31': [1, -4, 31], 'euler37': [1, -2, 37], 'euler41': [1, 3, 41], 'euler43': [1, -11, 43], 'euler47': [1, -12, 47], 'euler5': [1, 1, 0], 'euler53': [1, 0, 53], 'euler59': [1, 0, 59], 'euler61': [1, -7, 61], 'euler67': [1, -5, 67], 'euler7': [1, 0, 0], 'euler71': [1, 6, 71], 'euler73': [1, 2, 73], 'euler79': [1, 16, 79], 'euler83': [1, 9, 83], 'euler89': [1, 9, 89], 'euler97': [1, -4, 97], 'euler_factors': [[1, 0, 0], [1, 1, 3], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, -4, 13], [1, 6, 17], [1, 2, 19], [1, 9, 23], [1, -9, 29], [1, -4, 31], [1, -2, 37], [1, 3, 41], [1, -11, 43], [1, -12, 47], [1, 0, 53], [1, 0, 59], [1, -7, 61], [1, -5, 67], [1, 6, 71], [1, 2, 73], [1, 16, 79], [1, 9, 83], [1, 9, 89], [1, -4, 97]], 'index': 7, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/10780/e'], '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': '2-10780-1.1-c1-0-7', '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': '2-10780-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.27786254365413, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2139931915094694717, 'z1': {'__RealLiteral__': 0, 'data': '0.9646738707022310', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2139931915094694717', 'Lhash_array': ['2139931915094694717'], 'label': '2-10780-1.1-c1-0-7', 'type': 'ECQ', 'url': 'EllipticCurve/Q/10780/e'}