-
lfunc_lfunctions • Show schema
Hide schema
{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 0, 'Lhash': '351523239001231084', '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': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 436.9413998604465, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -1]], [19, [1, -1]]], 'bad_primes': [2, 3, 5, 19], 'central_character': '54720.1', 'coefficient_field': '1.1.1.1', 'conductor': 54720, 'conductor_radical': 570, 'degree': 2, 'euler_factors': [[1], [1], [1, -1], [1, -1, 7], [1, 0, 11], [1, -1, 13], [1, -3, 17], [1, -1], [1, -3, 23], [1, 3, 29], [1, 2, 31], [1, -10, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -3, 53], [1, 3, 59], [1, 8, 61], [1, 7, 67], [1, -12, 71], [1, 13, 73], [1, 14, 79], [1, 6, 83], [1, 6, 89], [1, 10, 97]], 'gamma_factors': [[], [0]], 'index': 116, 'label': '2-54720-1.1-c1-0-116', 'leading_term': '7.565024556', '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/54720/ef', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.760297915636039, 2.753821504258089, 2.446009805417879, 1.04871702691629, -0.2821506644223756, -0.24503030200483, 1.256719530624293, 2.694110226808851, 2.328983535221356, 0.2758613258193359, -1.277613195946713, -0.48133981602315, 1.718148154466899, 2.397461970004821, 0.2921933886871194, -2.285692049248403, -2.209425348019241, 0.2758057101205186, 1.743300935958895, 0.2868917697200826, -1.807903122340845, -1.526254713478175, 0.2396928578716368, 0.08359027130161238, -2.328365067872363, -3.318164885805751, -0.9244775348513743, 1.620355782931575, 0.7166503626162593, -1.828738010834672, -1.676533956737109, 0.8561456677716517, 1.270242144558351, -1.450696996090324, -2.933533369132048, -0.809814640087316, 1.231894857307632, -0.03830770199749761, -1.697159801061599, -0.08085790872284969, 2.321119451333133, 1.225956625002668, -1.506366344470461, -1.116664756685137, 1.264531312829817, 0.7284976832300109, -1.949067601308032, -1.375336480956906, 2.290108553469338, 3.164272130457351, 0.2835529988252073, -0.833669249088552, 1.306721649739808, 1.700176209542276, -1.002757045532857, -1.751527869031728, 0.8348851308497209, 1.759413790543547, -0.1392129291556773, 0.1774686493740982, 3.176960565720408, 2.840303493355775, -1.417949441466362, -2.661843280962349, 0.731350257264853, 2.340010839718596, 0.3722581120448381, 0.2914853616823743, 2.761870095192465, 2.263154914943227, -0.9732532623799881, -1.120585047150416, 1.213657485802717, 0.7398357083203032, -0.695496183045341, 1.913108358363272, 4.842578392012114, 2.099083463725304, -1.984022158296244, -0.7413974678866381, 2.003707821040951, 0.5230003408799812, -1.328557987235654, 0.5903029230425049, 1.817306052211688, -0.1120874917083155, 0.01624718386539668, 2.768569210249705, 1.738020112416313, -2.314664945566006, -2.127908163069126, 0.8166542526890203, -0.3605638006663826, -2.930330435707355, -0.7865385185747522, 1.885070898180063, -0.1627242635862264, -1.724517121327019, 1.053130202406854, 2.215016795458601, -0.3940168166261088, -0.6903752396357318, 1.19235897180817, -0.5713600164229389, -2.952672073349832, 0.06960597989887476, 3.442253217464443, 1.345650518052005, -0.5568979732106635, 1.535031222669361, 1.227309675388262, -2.5049344880101, -2.215390822230946, 1.166395976513351, 0.5172139961690612, -1.374461303968872, 0.8584735164908248, 2.037093363261703, -1.368728347582205, -2.5215118744313], 'positive_zeros': ['1.179394299638481', '1.556656691612980', '2.531211308155768', '3.057884605989019', '3.774533032361012', '4.474021709137856', '5.029277525330287', '5.708865021399140', '6.011998896196311', '6.820800737491836', '7.316625956126544', '7.914916730891531', '8.382785135703500', '9.069918060531283', '9.495922347979111', '10.00690669598835', '10.60123475162238', '11.10947699767783', '11.56695739185529', '12.09837321774314', '12.77500642479460', '13.11602061532459', '13.66421700826821', '14.17721160202023', '14.73005086048048', '14.98040427130096', '15.66876291870138', '16.20207235779642', '16.80780748701712', '16.95461280046040', '17.66828358357605', '18.11362360540527', '18.58788705527643', '18.86659977574702', '19.60520893650169'], 'prelabel': '2-54720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.903143300959464, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 351523239001231084, 'z1': {'__RealLiteral__': 0, 'data': '1.179394299638481', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.556656691612980', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.531211308155768', 'prec': 57}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 436.9413998604465, 'bad_primes': [2, 3, 5, 19], 'central_character': '1.1', 'conductor': 54720, 'conductor_radical': 570, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, 3, 0, 1, 0, 0, 0, -3, 0, -2, 0, 0, 0, 1, 0, 10, 0, 0, 0, -6, 0, 2, 0, 0, 0, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, -3, 0, -8, 0, 0, 0, 1, 0, -7, 0, 0, 0, 12, 0, -13, 0, 0, 0, 0, 0, -14, 0, 0, 0, -6, 0, 3, 0, 0, 0, -6, 0, 1, 0, 0, 0, 1, 0, -10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -1, 13], 'euler17': [1, -3, 17], 'euler19': [1, -1, 0], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 3, 29], 'euler3': [1, 0, 0], 'euler31': [1, 2, 31], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, -2, 43], 'euler47': [1, 0, 47], 'euler5': [1, -1, 0], 'euler53': [1, -3, 53], 'euler59': [1, 3, 59], 'euler61': [1, 8, 61], 'euler67': [1, 7, 67], 'euler7': [1, -1, 7], 'euler71': [1, -12, 71], 'euler73': [1, 13, 73], 'euler79': [1, 14, 79], 'euler83': [1, 6, 83], 'euler89': [1, 6, 89], 'euler97': [1, 10, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, -1, 0], [1, -1, 7], [1, 0, 11], [1, -1, 13], [1, -3, 17], [1, -1, 0], [1, -3, 23], [1, 3, 29], [1, 2, 31], [1, -10, 37], [1, 6, 41], [1, -2, 43], [1, 0, 47], [1, -3, 53], [1, 3, 59], [1, 8, 61], [1, 7, 67], [1, -12, 71], [1, 13, 73], [1, 14, 79], [1, 6, 83], [1, 6, 89], [1, 10, 97]], 'index': 116, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/54720/ef'], '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': '2-54720-1.1-c1-0-116', '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': '2-54720-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 20.903143300959464, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 351523239001231084, 'z1': {'__RealLiteral__': 0, 'data': '1.179394299638481', 'prec': 57}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '351523239001231084', 'Lhash_array': ['351523239001231084'], 'label': '2-54720-1.1-c1-0-116', 'type': 'ECQ', 'url': 'EllipticCurve/Q/54720/ef'}