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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1816891307267332954', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 366.2258838304005, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]], [13, [1, -1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '45864.1', 'coefficient_field': '1.1.1.1', 'conductor': 45864, 'conductor_radical': 546, 'degree': 2, 'euler_factors': [[1], [1], [1, 0, 5], [1], [1, -2, 11], [1, -1], [1, 6, 17], [1, -4, 19], [1, 4, 23], [1, 10, 29], [1, -8, 31], [1, 2, 37], [1, 0, 41], [1, 4, 43], [1, -2, 47], [1, -2, 53], [1, -10, 59], [1, 10, 61], [1, -8, 67], [1, 2, 71], [1, -10, 73], [1, -8, 79], [1, -6, 83], [1, 12, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 31, 'label': '2-45864-1.1-c1-0-31', 'leading_term': '5.8650970911', '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/45864/be', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.342792853010892, 1.961314099323753, 1.339421579085829, -0.3537054655039195, -2.037614377709648, -2.395743546721642, -1.154755425378743, 0.3348908797707416, 0.2196460870428199, -1.822480006946065, -3.887954161316883, -3.725840802649448, -1.394310774944698, 0.5764470272858832, 0.1617607953577843, -1.54243284964142, -1.686311737274053, 0.3917656705615994, 1.964557940787292, 0.5479584729411063, -2.399266924814964, -3.203025359579654, -1.10987014947894, 0.5889336923926779, -0.5658714593302944, -2.466559644193888, -1.751656913511266, 0.7269797988927336, 1.035757622975434, -1.505755687800285, -2.928145985407794, -0.8587379979265248, 1.512987703123969, 0.5279588252034256, -1.926009422312082, -1.602435977173467, 0.9123904038139641, 1.342101956010267, -0.6057975760537759, -0.5415072598192103, 2.674534136642187, 4.305245063089035, 1.607905951991503, -1.373138418752354, -0.7553786866878882, 0.7634366686649894, -0.4761748555377353, -1.939135075577838, 0.2314105264688328, 3.228661116498211, 1.914050006843814, -1.899364280520111, -2.516822537232286, -0.3738587612183189, -0.3631048914769744, -1.94758285657854, -0.3544345456327126, 3.34251864336254, 3.264109543786413, -0.3987965749524991, -1.673805901318939, 0.01840542819525832, -0.4838907173148214, -3.121810338544074, -2.467374757598377, 1.04790994062672, 1.289869716483018, -1.735968233760925, -1.973095537792814, 0.6703339715901014, 0.5690324914901237, -1.829216084561431, -1.118885423426495, 1.282543294962679, -0.460911594350522, -4.315208899027241, -3.744142706681774, -0.4135040495296485, -0.31954516742426, -1.638205368978671, 0.4036786419496657, 2.572127508592144, 0.5048498237329915, -1.162057823626646, 2.073471563301376, 4.750654941636982, 2.086976209536166, -0.7644150404734901, 0.139043870737536, 0.2271501869926163, -1.943782557011113, -0.6767343195270294, 3.638300315872251, 3.474729959998958, -0.7823969583553012, -1.574721970933847, 0.6013528805185417, -0.2044975273202319, -1.825632443068211, 0.2437509113060777, 1.373651361162286, -2.480155157074206, -4.902662220966061, -1.805262913831684, 0.4774854992331541, -0.6954193387488586, 0.5219826723014624, 3.825561206412539, 2.586837812880195, -0.9867354429682539, -0.04908612862745533, 2.109033133638849, -0.1115029267266563, -2.044323576748122, 0.04294779328520567, 0.05827005352652039, -3.626571727762379, -3.639613928956717, 0.0138118834434556, -0.1082161217492768], 'positive_zeros': ['0.9538840520714931', '1.927847454530567', '2.289340240890687', '3.397811362169130', '3.775596727057188', '4.460188409737115', '5.046990518632616', '5.870228192970721', '6.180121781822077', '6.921226857439713', '7.368642769481067', '8.070255934430190', '8.549971204535781', '9.156850351353414', '9.673219615989826', '10.05490011482517', '10.85822209276726', '11.34419387060851', '11.69480695011820', '12.23385534166068', '12.87003232975112', '13.57706048885360', '13.67086836852627', '14.27406818150711', '14.97159139342418', '15.49664978933443', '15.68842735265182', '16.41985994121248', '16.86058890680617', '17.43118549077096', '17.80893454202459', '18.34835309846994', '18.71981063434263', '19.55872165429016', '19.69313806721729'], 'prelabel': '2-45864-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.137029127594506, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1816891307267332954, 'z1': {'__RealLiteral__': 0, 'data': '0.9538840520714931', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.927847454530567', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.289340240890687', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 366.2258838304005, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 45864, 'conductor_radical': 546, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0, 0, -6, 0, 4, 0, 0, 0, -4, 0, -5, 0, 0, 0, -10, 0, 8, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, 2, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 10, 0, -10, 0, 0, 0, 0, 0, 8, 0, 0, 0, -2, 0, 10, 0, 0, 0, 0, 0, 8, 0, 0, 0, 6, 0, 0, 0, 0, 0, -12, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0], 'euler11': [1, -2, 11], 'euler13': [1, -1, 0], 'euler17': [1, 6, 17], 'euler19': [1, -4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 4, 23], 'euler29': [1, 10, 29], 'euler3': [1, 0, 0], 'euler31': [1, -8, 31], 'euler37': [1, 2, 37], 'euler41': [1, 0, 41], 'euler43': [1, 4, 43], 'euler47': [1, -2, 47], 'euler5': [1, 0, 5], 'euler53': [1, -2, 53], 'euler59': [1, -10, 59], 'euler61': [1, 10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 0, 0], 'euler71': [1, 2, 71], 'euler73': [1, -10, 73], 'euler79': [1, -8, 79], 'euler83': [1, -6, 83], 'euler89': [1, 12, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 5], [1, 0, 0], [1, -2, 11], [1, -1, 0], [1, 6, 17], [1, -4, 19], [1, 4, 23], [1, 10, 29], [1, -8, 31], [1, 2, 37], [1, 0, 41], [1, 4, 43], [1, -2, 47], [1, -2, 53], [1, -10, 59], [1, 10, 61], [1, -8, 67], [1, 2, 71], [1, -10, 73], [1, -8, 79], [1, -6, 83], [1, 12, 89], [1, -2, 97]], 'index': 31, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/45864/be'], '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': '2-45864-1.1-c1-0-31', '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': '2-45864-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.137029127594506, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1816891307267332954, 'z1': {'__RealLiteral__': 0, 'data': '0.9538840520714931', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1816891307267332954', 'Lhash_array': ['1816891307267332954'], 'label': '2-45864-1.1-c1-0-31', 'type': 'ECQ', 'url': 'EllipticCurve/Q/45864/be'}