-
nf_fields • Show schema
{'cm': True, 'coeffs': [361, 0, 5415, 0, 57399, 0, 262086, 0, 806113, 0, 1629193, 0, 2415451, 0, 2670317, 0, 2298126, 0, 1558038, 0, 848787, 0, 372723, 0, 132810, 0, 38095, 0, 8740, 0, 1558, 0, 209, 0, 19, 0, 1], 'conductor': 228, 'degree': 36, 'dirichlet_group': [1, 5, 137, 143, 17, 149, 151, 25, 155, 157, 31, 161, 167, 169, 49, 179, 59, 61, 67, 197, 71, 73, 203, 77, 79, 211, 85, 91, 223, 227, 101, 103, 107, 121, 125, 127], 'disc_abs': 799622233646074762983150698451178476894456963777140963130998784, 'disc_rad': 114, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[18, 2]]], [7, [[6, 6]]], [11, [[6, 6]]], [13, [[18, 2]]], [17, [[18, 2]]], [19, [0]], [23, [[18, 2]]], [29, [[18, 2]]], [31, [[3, 12]]], [37, [[2, 18]]], [41, [[18, 2]]], [43, [[18, 2]]], [47, [[18, 2]]], [53, [[18, 2]]], [59, [[18, 2]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [36, 18, 34], 'galois_label': '36T2', 'galt': 2, 'grd': 55.88591389129187, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '36.0.799622233646074762983150698451178476894456963777140963130998784.2', 'local_algs': ['m2.2.18.36', 'm3.2.9.9', 'm3.2.9.9', '19.18.17.1', '19.18.17.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 18, 'ramps': [2, 3, 19], 'rd': 55.8859138913, 'res': {'ae': []}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.-1.1', '-19.0.1', '57.0.1', '7.-6.-1.1', '361.0.19.0.1', '49.-42.43.-8.7.-1.1', '-19.0.38.0.-19.0.1', '513.0.342.0.57.0.1', '-1.5.10.-20.-15.21.7.-8.-1.1', '361.0.722.0.1083.0.684.0.323.0.19.0.1', '1.-5.35.10.185.-71.431.-77.494.-118.361.-63.162.-29.50.-6.9.-1.1', '-19.0.285.0.-1254.0.2508.0.-2717.0.1729.0.-665.0.152.0.-19.0.1', '373977.0.1869885.0.2742498.0.1828332.0.660231.0.140049.0.17955.0.1368.0.57.0.1'], 'torsion_gen': '\\( \\frac{26829997518280183021}{66495926797178861491219} a^{34} + \\frac{26598244133079038772}{3499785620904150604801} a^{32} + \\frac{290816878133015963118}{3499785620904150604801} a^{30} + \\frac{2153288311705603483287}{3499785620904150604801} a^{28} + \\frac{11998687105984961447667}{3499785620904150604801} a^{26} + \\frac{51899600479398829656543}{3499785620904150604801} a^{24} + \\frac{4849522942561243997067}{94588800564977043373} a^{22} + \\frac{498605177959280803164861}{3499785620904150604801} a^{20} + \\frac{1122593033140817945162022}{3499785620904150604801} a^{18} + \\frac{2031702862437939905122865}{3499785620904150604801} a^{16} + \\frac{155072516601073134700314}{184199243205481610779} a^{14} + \\frac{176194500030210489789879}{184199243205481610779} a^{12} + \\frac{155039966107495776853800}{184199243205481610779} a^{10} + \\frac{100425776080331302112142}{184199243205481610779} a^{8} + \\frac{47425533042550358380716}{184199243205481610779} a^{6} + \\frac{14082041180781203080581}{184199243205481610779} a^{4} + \\frac{3119154647880984572367}{184199243205481610779} a^{2} + \\frac{291248148377115816489}{184199243205481610779} \\)', 'torsion_order': 6, 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', 'a^12', 'a^13', 'a^14', 'a^15', 'a^16', 'a^17', '1/19*a^18', '1/19*a^19', '1/19*a^20', '1/19*a^21', '1/19*a^22', '1/19*a^23', '1/19*a^24', '1/19*a^25', '1/703*a^26 + 3/703*a^24 + 12/703*a^22 - 1/703*a^18 - 6/37*a^16 - 7/37*a^14 - 2/37*a^12 + 10/37*a^10 - 1/37*a^8 - 10/37*a^6 + 4/37*a^4 - 3/37*a^2 + 3/37', '1/703*a^27 + 3/703*a^25 + 12/703*a^23 - 1/703*a^19 - 6/37*a^17 - 7/37*a^15 - 2/37*a^13 + 10/37*a^11 - 1/37*a^9 - 10/37*a^7 + 4/37*a^5 - 3/37*a^3 + 3/37*a', '1/703*a^28 + 3/703*a^24 + 1/703*a^22 - 1/703*a^20 + 11/37*a^16 - 18/37*a^14 + 16/37*a^12 + 6/37*a^10 - 7/37*a^8 - 3/37*a^6 - 15/37*a^4 + 12/37*a^2 - 9/37', '1/703*a^29 + 3/703*a^25 + 1/703*a^23 - 1/703*a^21 + 11/37*a^17 - 18/37*a^15 + 16/37*a^13 + 6/37*a^11 - 7/37*a^9 - 3/37*a^7 - 15/37*a^5 + 12/37*a^3 - 9/37*a', '1/703*a^30 - 8/703*a^24 - 10/703*a^18 + 12/37*a^12 + 15/37*a^6 - 9/37', '1/703*a^31 - 8/703*a^25 - 10/703*a^19 + 12/37*a^13 + 15/37*a^7 - 9/37*a', '1/703*a^32 - 13/703*a^24 - 15/703*a^22 - 10/703*a^20 - 8/703*a^18 - 11/37*a^16 - 7/37*a^14 - 16/37*a^12 + 6/37*a^10 + 7/37*a^8 - 6/37*a^6 - 5/37*a^4 + 4/37*a^2 - 13/37', '1/703*a^33 - 13/703*a^25 - 15/703*a^23 - 10/703*a^21 - 8/703*a^19 - 11/37*a^17 - 7/37*a^15 - 16/37*a^13 + 6/37*a^11 + 7/37*a^9 - 6/37*a^7 - 5/37*a^5 + 4/37*a^3 - 13/37*a', '1/66495926797178861491219*a^34 + 95473288288552618/184199243205481610779*a^32 + 1807951731514635866/3499785620904150604801*a^30 + 171309968879160652/3499785620904150604801*a^28 + 440090776031058913/3499785620904150604801*a^26 - 53585764503177685364/3499785620904150604801*a^24 + 26683600630186601723/3499785620904150604801*a^22 + 32781662307927217072/3499785620904150604801*a^20 + 91988776569193916607/3499785620904150604801*a^18 - 1307974449556231788942/3499785620904150604801*a^16 - 30943815699806536848/184199243205481610779*a^14 - 43424296143470230158/184199243205481610779*a^12 - 71260072058689014988/184199243205481610779*a^10 - 55846283841363957147/184199243205481610779*a^8 + 26505569839203403346/184199243205481610779*a^6 - 34104452947850036366/184199243205481610779*a^4 - 38520759123752461115/184199243205481610779*a^2 + 65912108193554012131/184199243205481610779', '1/66495926797178861491219*a^35 + 95473288288552618/184199243205481610779*a^33 + 1807951731514635866/3499785620904150604801*a^31 + 171309968879160652/3499785620904150604801*a^29 + 440090776031058913/3499785620904150604801*a^27 - 53585764503177685364/3499785620904150604801*a^25 + 26683600630186601723/3499785620904150604801*a^23 + 32781662307927217072/3499785620904150604801*a^21 + 91988776569193916607/3499785620904150604801*a^19 - 1307974449556231788942/3499785620904150604801*a^17 - 30943815699806536848/184199243205481610779*a^15 - 43424296143470230158/184199243205481610779*a^13 - 71260072058689014988/184199243205481610779*a^11 - 55846283841363957147/184199243205481610779*a^9 + 26505569839203403346/184199243205481610779*a^7 - 34104452947850036366/184199243205481610779*a^5 - 38520759123752461115/184199243205481610779*a^3 + 65912108193554012131/184199243205481610779*a']}
Number field data - 36.0.799622233646074762983150698451178476894456963777140963130998784.2