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lfunc_lfunctions • Show schema
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{'A10': -2, 'A2': -1, 'A3': -1, 'A4': 1, 'A5': 2, 'A6': 1, 'A7': 0, 'A8': -1, 'A9': 1, 'Lhash': '1332805508042216290', 'a10': [-0.6324555320336759, 0], 'a2': [-0.7071067811865475, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.5, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.4082482904638631, 0], 'a7': [0.0, 0], 'a8': [-0.35355339059327373, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 89.06513841453618, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 1]], [3, [1, 1]], [11, [1, 1]], [13, [1]]], 'bad_primes': [2, 3, 11, 13], 'central_character': '11154.1', 'coefficient_field': '1.1.1.1', 'conductor': 11154, 'conductor_radical': 858, 'degree': 2, 'euler_factors': [[1, 1], [1, 1], [1, -2, 5], [1, 0, 7], [1, 1], [1], [1, -6, 17], [1, 0, 19], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 4, 59], [1, 2, 61], [1, -4, 67], [1, -8, 71], [1, 14, 73], [1, 8, 79], [1, 4, 83], [1, -6, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 25, 'label': '2-11154-1.1-c1-0-25', 'leading_term': '3.37766684343', '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/11154/j', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.8050866129116495, 1.36108677297645, 1.411874515225651, 0.8582995190875883, -0.02069213256228222, -0.5745958502183098, -0.1746039939814547, 1.196649057356479, 2.668982713936619, 2.964851742651655, 1.489444437288167, -0.8315768189845231, -1.925494470611392, -0.2072147526517884, 3.783315029979065, 7.394585051831886, 7.909901162986468, 4.977308509124177, 1.044656554040153, -0.8708489554115028, -0.01005991958584169, 1.620439665683155, 1.652812052981083, 0.03155738631300121, -1.114387021314595, -0.2632783872577503, 1.454240561460244, 1.6049261158131, -0.3664277191099887, -2.211101807483918, -1.626968902719959, 0.6962617907323431, 1.791667725908591, 0.1828102578188942, -2.167730743832858, -2.392310511964478, -0.4119558909397461, 1.18667382547904, 0.8283496413253605, -0.07609380170654768, 0.3664410038584052, 1.404686884575061, 0.7881035359333272, -1.408720054203371, -2.343691773210932, -0.5831605770185899, 1.28505788531947, 0.1433636724186623, -2.772112254120692, -3.255620341883352, -0.4463284184718059, 1.346321672363012, -1.203619234613193, -5.052123556451526, -4.715624126506434, -0.3642576358703948, 2.024725142964734, -0.7667287457645414, -4.43147661373109, -3.419366991367421, 1.019302378239145, 2.951193208267822, 0.4876206801517945, -2.12847668884837, -1.485473156259867, 0.3835710867622463, 0.2961767018872873, -0.9105091705605416, -0.6944051109969464, 0.3642462614114985, -0.058611594509644, -1.387305280594144, -1.095026262516746, 0.3674250472443471, 0.09058841481762046, -1.627949154724389, -0.9947782803335795, 2.498028376035073, 3.976998328294791, 0.703290051045584, -2.909624131393282, -1.923160206376402, 1.412816756704638, 1.863631770963251, 0.00814306180734335, 0.2968557844434393, 2.145725495067435, 0.5917243328484927, -4.083487677789741, -5.364336426747744, -1.152596458438463, 2.275315745069944, 0.5750849697413871, -1.659334916996978, 0.5975466905035682, 3.810263366484077, 2.198444872901238, -2.090337031601171, -2.886397291715162, -0.42629371526927, 0.2572198445202422, -1.119952041764661, -0.5724088265554689, 1.514940495417202, 0.7521933285113667, -2.54171174876019, -3.270828305919202, -0.6340597204814751, 0.7345768988845206, -0.51024004561456, -0.5359567396006188, 1.647765633827282, 2.227941815317084, 0.189291802322258, -0.8807545383235262, -0.06274533445613795, -0.3533051105414835, -1.529423696426351, -0.2148484477617318, 2.062364560345354], 'positive_zeros': ['1.243886444881757', '1.791801190991859', '2.907982770143993', '3.516001517083775', '4.841529390259386', '5.251458434767349', '6.004398862039332', '6.537614721440746', '7.212105058052368', '7.926474242724361', '8.517884980864016', '9.296611057349563', '9.961815927772440', '10.14787272199259', '10.84664643376246', '11.55891583548420', '12.01317989011360', '12.78572549535060', '13.17197585094506', '14.02086789859410', '14.45513675290881', '15.19192778695079', '15.78529741850852', '16.43369239219527', '16.80914641646317', '17.39696455611158', '17.73847598053696', '18.42651626048696', '18.76457321402482', '19.33150721901002'], 'prelabel': '2-11154-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.437432829670163, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1332805508042216290, 'z1': {'__RealLiteral__': 0, 'data': '1.243886444881757', 'prec': 57}, 'z2': {'__RealLiteral__': 0, 'data': '1.791801190991859', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.907982770143993', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 89.06513841453618, 'bad_primes': [2, 3, 11, 13], 'central_character': '1.1', 'conductor': 11154, 'conductor_radical': 858, 'degree': 2, 'dirichlet_coefficients': [1, -1, -1, 1, 2, 1, 0, -1, 1, -2, -1, -1, 0, 0, -2, 1, 6, -1, 0, 2, 0, 1, 4, 1, -1, 0, -1, 0, 6, 2, -4, -1, 1, -6, 0, 1, -2, 0, 0, -2, -10, 0, -4, -1, 2, -4, -8, -1, -7, 1, -6, 0, -6, 1, -2, 0, 0, -6, -4, -2, -2, 4, 0, 1, 0, -1, 4, 6, -4, 0, 8, -1, -14, 2, 1, 0, 0, 0, -8, 2, 1, 10, -4, 0, 12, 4, -6, 1, 6, -2, 0, 4, 4, 8, 0, 1, -2, 7, -1, -1], 'euler11': [1, 1, 0], 'euler13': [1, 0, 0], 'euler17': [1, -6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 1, 0], 'euler23': [1, -4, 23], 'euler29': [1, -6, 29], 'euler3': [1, 1, 0], 'euler31': [1, 4, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, 4, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 2, 61], 'euler67': [1, -4, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, 14, 73], 'euler79': [1, 8, 79], 'euler83': [1, 4, 83], 'euler89': [1, -6, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 1, 0], [1, 1, 0], [1, -2, 5], [1, 0, 7], [1, 1, 0], [1, 0, 0], [1, -6, 17], [1, 0, 19], [1, -4, 23], [1, -6, 29], [1, 4, 31], [1, 2, 37], [1, 10, 41], [1, 4, 43], [1, 8, 47], [1, 6, 53], [1, 4, 59], [1, 2, 61], [1, -4, 67], [1, -8, 71], [1, 14, 73], [1, 8, 79], [1, 4, 83], [1, -6, 89], [1, 2, 97]], 'index': 25, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/11154/j'], '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': '2-11154-1.1-c1-0-25', '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': '2-11154-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 9.437432829670163, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1332805508042216290, 'z1': {'__RealLiteral__': 0, 'data': '1.243886444881757', 'prec': 57}}
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lfunc_instances • Show schema
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{'Lhash': '1332805508042216290', 'Lhash_array': ['1332805508042216290'], 'label': '2-11154-1.1-c1-0-25', 'type': 'ECQ', 'url': 'EllipticCurve/Q/11154/j'}