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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1969527022953468297', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 285.06593521597114, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [7, [1, 1]], [17, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '35700.1', 'coefficient_field': '1.1.1.1', 'conductor': 35700, 'conductor_radical': 3570, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1], [1, 0, 11], [1, 2, 13], [1, -1], [1, -2, 19], [1, 6, 23], [1, 6, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 2, 43], [1, 0, 47], [1, 0, 53], [1, -12, 59], [1, -8, 61], [1, 14, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -12, 83], [1, 0, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-35700-1.1-c1-0-19', 'leading_term': '4.1333275593', '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/35700/i', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9310399739323113, 1.26326585159599, 0.5751839723728055, -0.9716947035873186, -2.415133863025146, -2.532220869159844, -0.9785550905874831, 1.034263734715372, 1.54172197800479, -0.258472310455507, -2.870057698348828, -3.722119096086736, -1.880372792976735, 0.7191434557271335, 1.29534907743403, -0.5170252406325665, -2.138829429239068, -1.22218449636637, 1.307028130941137, 2.418553982786403, 1.020494141083254, -0.6106525940750761, -0.1647032225963304, 1.28168695832405, 0.9069145624457132, -1.368145135209652, -2.423382946769715, -0.6416123302688764, 1.332886048785125, 0.5393999619764274, -1.370190878321159, -0.3221048944096185, 3.549553240386905, 5.260733564456351, 2.147175044410281, -1.923028668975708, -2.171448968021193, 0.1799538717688346, 0.5436408312339085, -1.381436801159354, -1.60771179121886, 0.801331353919215, 1.87542781143469, -0.3386077151183105, -2.240759460264675, -0.9039261187292101, 0.9252734067461421, 0.02502546749668965, -1.354407460863626, 0.1779669996248122, 2.472878222206696, 1.629011219627823, -0.3128473062981152, 1.41152600190842, 5.134581614298285, 4.796557006942809, 0.5892753054565584, -1.021424218693021, 1.383383668381295, 1.850326228525632, -1.904215269742131, -4.276321327953434, -1.951489147423433, 0.5737305416667868, -0.1409836329996731, -0.7074799798789786, 1.230397945521703, 1.87918672896317, -0.7584092516269758, -2.222605043203706, -0.1697200704155362, 0.9681740253720843, -0.9383462796423094, -1.186815096003644, 1.969328608946634, 2.952813145556966, -0.301671880542236, -1.78440473512196, 0.8426849274660595, 1.383169343308304, -2.46438835347804, -4.061335730458699, -0.8651037009375543, 0.3002441862640608, -3.421414191649636, -5.403436214559931, -2.422617073999196, 0.1149305457328519, -0.19780357404611, 0.7352362058657879, 2.894791634058629, 1.577476393132633, -1.757369649230749, -1.530073240096092, 0.5484343784378123, -0.5430656529877995, -1.962911630665974, 0.7161306862333338, 2.898846669092865, 0.01282436113800081, -2.129397137221189, 1.220795337324521, 3.63364290033714, 0.5303174723290964, -1.571301055961954, 1.046773023707067, 1.886012350710256, -1.321289635572904, -1.758568439035942, 1.651356273369529, 2.13502722122108, -0.4060684938660309, -0.1765825416907913, 1.32105069380429, -0.5524563427245132, -2.363764713826032, -0.294376554712568, 1.052705363225069, -0.7392397431589866, -0.4692682952654475], 'positive_zeros': ['0.8535781618680735', '1.863644076304356', '2.474924835870661', '3.420345825331447', '3.942910259589573', '4.622508688036923', '5.379762895483012', '5.777811829652884', '6.358919216468836', '7.062899332699531', '7.562163342710675', '8.025139721303073', '8.865949895978221', '9.478223786336379', '9.831492751448618', '10.42504278276694', '10.97099271581144', '11.59564307618421', '12.00325244667616', '12.48353741769818', '13.18104118352078', '13.37683471156656', '14.29021946638638', '14.62679711610428', '15.14052119859881', '15.90839447920377', '16.22671383564232', '16.61433136131880', '17.18928139164978', '17.76690154776408', '18.14625754377725', '18.60836351674973', '19.22930554671321', '19.68104251547625'], 'prelabel': '2-35700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.88389573575871, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1969527022953468297, 'z1': {'__RealLiteral__': 0, 'data': '0.8535781618680735', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.863644076304356', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.474924835870661', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 285.06593521597114, 'bad_primes': [2, 3, 5, 7, 17], 'central_character': '1.1', 'conductor': 35700, 'conductor_radical': 3570, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 0, 0, -2, 0, 0, 0, 1, 0, 2, 0, 1, 0, -6, 0, 0, 0, -1, 0, -6, 0, -4, 0, 0, 0, 0, 0, 4, 0, 2, 0, 6, 0, -2, 0, 0, 0, 0, 0, 1, 0, -1, 0, 0, 0, 0, 0, -2, 0, 12, 0, 8, 0, -1, 0, 0, 0, -14, 0, 6, 0, 0, 0, -2, 0, 0, 0, 0, 0, 8, 0, 1, 0, 12, 0, 0, 0, 6, 0, 0, 0, 2, 0, 4, 0, 0, 0, 10, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 2, 13], 'euler17': [1, -1, 0], 'euler19': [1, -2, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, 6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, -4, 37], 'euler41': [1, -6, 41], 'euler43': [1, 2, 43], 'euler47': [1, 0, 47], 'euler5': [1, 0, 0], 'euler53': [1, 0, 53], 'euler59': [1, -12, 59], 'euler61': [1, -8, 61], 'euler67': [1, 14, 67], 'euler7': [1, 1, 0], 'euler71': [1, 0, 71], 'euler73': [1, 2, 73], 'euler79': [1, -8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 0, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 0], [1, 0, 11], [1, 2, 13], [1, -1, 0], [1, -2, 19], [1, 6, 23], [1, 6, 29], [1, 4, 31], [1, -4, 37], [1, -6, 41], [1, 2, 43], [1, 0, 47], [1, 0, 53], [1, -12, 59], [1, -8, 61], [1, 14, 67], [1, 0, 71], [1, 2, 73], [1, -8, 79], [1, -12, 83], [1, 0, 89], [1, -10, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/35700/i'], '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': '2-35700-1.1-c1-0-19', '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': '2-35700-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 16.88389573575871, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1969527022953468297, 'z1': {'__RealLiteral__': 0, 'data': '0.8535781618680735', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1969527022953468297', 'Lhash_array': ['1969527022953468297'], 'factors': ['2-35700-1.1-c1-0-19'], 'label': '2-35700-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/35700/i'}