-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [-2197, 0, 13689, 0, -33462, 0, 42276, 0, -30537, 0, 13113, 0, -3345, 0, 486, 0, -36, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 45459928664503948293335446409613, 'disc_rad': 39, 'disc_sign': 1, 'frobs': [[2, [[4, 4], [2, 1]]], [3, [0]], [5, [[4, 4], [2, 1]]], [7, [[4, 4], [2, 1]]], [11, [[4, 4], [2, 1]]], [13, [0]], [17, [[3, 6]]], [19, [[4, 4], [2, 1]]], [23, [[3, 6]]], [29, [[2, 8], [1, 2]]], [31, [[4, 4], [2, 1]]], [37, [[4, 4], [2, 1]]], [41, [[4, 4], [2, 1]]], [43, [[2, 8], [1, 2]]], [47, [[4, 4], [2, 1]]], [53, [[2, 8], [1, 2]]], [59, [[4, 4], [2, 1]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [74, 27], 'galois_label': '18T10', 'galt': 10, 'grd': 65.49479091539757, 'inessentialp': [2], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.18.45459928664503948293335446409613.1', 'local_algs': ['3.9.18.2', '3.9.18.2', '13.2.1.1', '13.4.3.2', '13.4.3.2', '13.4.3.2', '13.4.3.2'], 'minimal_sibling': [-9, 9, 27, -9, -15, 0, 1], 'monogenic': -1, 'num_ram': 2, 'r2': 0, 'ramps': [3, 13], 'rd': 57.3795519567, 'regulator': {'__RealLiteral__': 0, 'data': '40148447797.4', 'prec': 44}, 'res': {'sib': ['-9,81,81,-9,-18,0,1', '-9,9,27,-9,-15,0,1', '1,-6,-12,115,-96,-372,741,-372,-96,115,-12,-6,1', '117,0,-3159,0,7263,0,-2955,0,486,0,-36,0,1', '1339,819,-1404,-858,459,297,-45,-36,0,1']}, 'subfield_mults': [1, 2, 2, 1], 'subfields': ['-3.-1.1', '-9.9.27.-9.-15.0.1', '-9.81.81.-9.-18.0.1', '1339.819.-1404.-858.459.297.-45.-36.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{11689}{813397} a^{17} - \\frac{1217}{1626794} a^{16} - \\frac{31436}{62569} a^{15} + \\frac{75831}{1626794} a^{14} + \\frac{5274833}{813397} a^{13} - \\frac{1642317}{1626794} a^{12} - \\frac{68437991}{1626794} a^{11} + \\frac{16235303}{1626794} a^{10} + \\frac{124581993}{813397} a^{9} - \\frac{82590515}{1626794} a^{8} - \\frac{529292001}{1626794} a^{7} + \\frac{17282285}{125138} a^{6} + \\frac{49659913}{125138} a^{5} - \\frac{24777121}{125138} a^{4} - \\frac{31535165}{125138} a^{3} + \\frac{664635}{4813} a^{2} + \\frac{596319}{9626} a - \\frac{172300}{4813} \\)', '\\( \\frac{28142}{813397} a^{17} + \\frac{41775}{813397} a^{16} - \\frac{148381}{125138} a^{15} - \\frac{2835095}{1626794} a^{14} + \\frac{24022373}{1626794} a^{13} + \\frac{17370539}{813397} a^{12} - \\frac{73416390}{813397} a^{11} - \\frac{207493815}{1626794} a^{10} + \\frac{485429221}{1626794} a^{9} + \\frac{331985344}{813397} a^{8} - \\frac{443733157}{813397} a^{7} - \\frac{44560703}{62569} a^{6} + \\frac{33518622}{62569} a^{5} + \\frac{40807865}{62569} a^{4} - \\frac{32356839}{125138} a^{3} - \\frac{1357414}{4813} a^{2} + \\frac{230692}{4813} a + \\frac{211338}{4813} \\)', '\\( \\frac{5488}{813397} a^{17} - \\frac{6001}{813397} a^{16} - \\frac{418683}{1626794} a^{15} + \\frac{204414}{813397} a^{14} + \\frac{3046463}{813397} a^{13} - \\frac{5032081}{1626794} a^{12} - \\frac{45161477}{1626794} a^{11} + \\frac{15053720}{813397} a^{10} + \\frac{14351229}{125138} a^{9} - \\frac{47912729}{813397} a^{8} - \\frac{217118218}{813397} a^{7} + \\frac{12681237}{125138} a^{6} + \\frac{20878017}{62569} a^{5} - \\frac{11649923}{125138} a^{4} - \\frac{12452299}{62569} a^{3} + \\frac{440227}{9626} a^{2} + \\frac{217805}{4813} a - \\frac{82265}{9626} \\)', '\\( \\frac{158515}{1626794} a^{17} + \\frac{138207}{1626794} a^{16} - \\frac{5620547}{1626794} a^{15} - \\frac{4896581}{1626794} a^{14} + \\frac{73923315}{1626794} a^{13} + \\frac{64321875}{1626794} a^{12} - \\frac{243985538}{813397} a^{11} - \\frac{211944390}{813397} a^{10} + \\frac{894470998}{813397} a^{9} + \\frac{1550871839}{1626794} a^{8} - \\frac{1866815518}{813397} a^{7} - \\frac{248461851}{125138} a^{6} + \\frac{330212227}{125138} a^{5} + \\frac{285309051}{125138} a^{4} - \\frac{93370005}{62569} a^{3} - \\frac{6214273}{4813} a^{2} + \\frac{1455417}{4813} a + \\frac{1266007}{4813} \\)', '\\( \\frac{36917}{1626794} a^{17} - \\frac{1255351}{1626794} a^{15} + \\frac{7726365}{813397} a^{13} - \\frac{46590446}{813397} a^{11} + \\frac{900444}{4813} a^{9} - \\frac{277214229}{813397} a^{7} + \\frac{21237570}{62569} a^{5} - \\frac{10556798}{62569} a^{3} + \\frac{1}{2} a^{2} + \\frac{152154}{4813} a - \\frac{1}{2} \\)', '\\( \\frac{4611}{1626794} a^{16} - \\frac{79878}{813397} a^{14} + \\frac{1012131}{813397} a^{12} - \\frac{6336842}{813397} a^{10} + \\frac{21651274}{813397} a^{8} - \\frac{3201219}{62569} a^{6} + \\frac{3484878}{62569} a^{4} - \\frac{168627}{4813} a^{2} + \\frac{1}{2} a + \\frac{49837}{4813} \\)', '\\( \\frac{6593}{813397} a^{17} - \\frac{83071}{1626794} a^{16} - \\frac{227859}{813397} a^{15} + \\frac{1443343}{813397} a^{14} + \\frac{2876738}{813397} a^{13} - \\frac{36812547}{1626794} a^{12} - \\frac{2757973}{125138} a^{11} + \\frac{233461999}{1626794} a^{10} + \\frac{60775867}{813397} a^{9} - \\frac{408047586}{813397} a^{8} - \\frac{228827253}{1626794} a^{7} + \\frac{124543853}{125138} a^{6} + \\frac{8899648}{62569} a^{5} - \\frac{68429445}{62569} a^{4} - \\frac{4417193}{62569} a^{3} + \\frac{2895075}{4813} a^{2} + \\frac{138881}{9626} a - \\frac{1176453}{9626} \\)', '\\( \\frac{8575}{1626794} a^{17} + \\frac{383}{62569} a^{16} - \\frac{147981}{813397} a^{15} - \\frac{13420}{62569} a^{14} + \\frac{1864607}{813397} a^{13} + \\frac{347681}{125138} a^{12} - \\frac{23179965}{1626794} a^{11} - \\frac{2264209}{125138} a^{10} + \\frac{39124593}{813397} a^{9} + \\frac{316683}{4813} a^{8} - \\frac{145595559}{1626794} a^{7} - \\frac{17179999}{125138} a^{6} + \\frac{5414770}{62569} a^{5} + \\frac{9924493}{62569} a^{4} - \\frac{2225042}{62569} a^{3} - \\frac{860771}{9626} a^{2} + \\frac{12384}{4813} a + \\frac{165989}{9626} \\)', '\\( \\frac{5488}{813397} a^{17} + \\frac{6001}{813397} a^{16} - 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\\frac{5056998}{62569} a^{4} - \\frac{41171333}{125138} a^{3} + \\frac{404243}{9626} a^{2} + \\frac{641535}{9626} a - \\frac{71233}{9626} \\)', '\\( \\frac{1471}{1626794} a^{17} + \\frac{24316}{813397} a^{16} - \\frac{45815}{813397} a^{15} - \\frac{1619439}{1626794} a^{14} + \\frac{152725}{125138} a^{13} + \\frac{19220781}{1626794} a^{12} - \\frac{19621423}{1626794} a^{11} - \\frac{54706559}{813397} a^{10} + \\frac{49633812}{813397} a^{9} + \\frac{163317091}{813397} a^{8} - \\frac{264515255}{1626794} a^{7} - \\frac{19951556}{62569} a^{6} + \\frac{27506805}{125138} a^{5} + \\frac{2520587}{9626} a^{4} - \\frac{16704999}{125138} a^{3} - \\frac{1018691}{9626} a^{2} + \\frac{267445}{9626} a + \\frac{161305}{9626} \\)', '\\( \\frac{4865}{1626794} a^{17} + \\frac{22305}{1626794} a^{16} - \\frac{175555}{1626794} a^{15} - \\frac{771533}{1626794} a^{14} + \\frac{1183685}{813397} a^{13} + \\frac{9790467}{1626794} a^{12} - \\frac{8029902}{813397} a^{11} - \\frac{62015357}{1626794} a^{10} + \\frac{59979657}{1626794} a^{9} + \\frac{109175748}{813397} a^{8} - \\frac{61538622}{813397} a^{7} - \\frac{33964669}{125138} a^{6} + \\frac{4849720}{62569} a^{5} + \\frac{19202423}{62569} a^{4} - \\frac{1873111}{62569} a^{3} - \\frac{848396}{4813} a^{2} + \\frac{4040}{4813} a + \\frac{191286}{4813} \\)', '\\( \\frac{39401}{813397} a^{17} - \\frac{21981}{1626794} a^{16} - \\frac{1344977}{813397} a^{15} + \\frac{785791}{1626794} a^{14} + \\frac{33284363}{1626794} a^{13} - \\frac{5202439}{813397} a^{12} - \\frac{100803624}{813397} a^{11} + \\frac{68392511}{1626794} a^{10} + \\frac{658485135}{1626794} a^{9} - \\frac{122050179}{813397} a^{8} - \\frac{592842052}{813397} a^{7} + \\frac{18398301}{62569} a^{6} + \\frac{43991841}{62569} a^{5} - \\frac{19015095}{62569} a^{4} - \\frac{41455539}{125138} a^{3} + \\frac{718292}{4813} a^{2} + \\frac{553101}{9626} a - \\frac{248185}{9626} \\)', '\\( \\frac{10737}{813397} a^{17} + \\frac{53375}{1626794} a^{16} - \\frac{27190}{62569} a^{15} - \\frac{1866081}{1626794} a^{14} + \\frac{4109330}{813397} a^{13} + \\frac{24014261}{1626794} a^{12} - \\frac{22579200}{813397} a^{11} - \\frac{77006443}{813397} a^{10} + \\frac{63129786}{813397} a^{9} + \\frac{272610383}{813397} a^{8} - \\frac{173878729}{1626794} a^{7} - \\frac{6484645}{9626} a^{6} + \\frac{3635702}{62569} a^{5} + \\frac{93773877}{125138} a^{4} + \\frac{154547}{62569} a^{3} - \\frac{1997599}{4813} a^{2} - \\frac{33216}{4813} a + \\frac{400832}{4813} \\)', '\\( \\frac{33589}{1626794} a^{17} + \\frac{17963}{813397} a^{16} - \\frac{1108983}{1626794} a^{15} - \\frac{592601}{813397} a^{14} + \\frac{12956343}{1626794} a^{13} + \\frac{6926060}{813397} a^{12} - \\frac{71756549}{1626794} a^{11} - \\frac{38546782}{813397} a^{10} + \\frac{203731043}{1626794} a^{9} + \\frac{111053435}{813397} a^{8} - \\frac{145815795}{813397} a^{7} - \\frac{12702590}{62569} a^{6} + \\frac{6970502}{62569} a^{5} + \\frac{17960185}{125138} a^{4} - \\frac{1285423}{125138} a^{3} - \\frac{349449}{9626} a^{2} - \\frac{92487}{9626} a - \\frac{11469}{9626} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/2*a^9 - 1/2*a^6 - 1/2*a^5 - 1/2*a^4 - 1/2*a - 1/2', '1/2*a^10 - 1/2*a^7 - 1/2*a^6 - 1/2*a^5 - 1/2*a^2 - 1/2*a', '1/2*a^11 - 1/2*a^8 - 1/2*a^7 - 1/2*a^6 - 1/2*a^3 - 1/2*a^2', '1/26*a^12 + 3/26*a^10 + 5/26*a^8 - 2/13*a^6 - 2/13*a^4 - 1/2*a^3 - 1/2*a^2 - 1/2', '1/26*a^13 + 3/26*a^11 + 5/26*a^9 - 2/13*a^7 - 2/13*a^5 - 1/2*a^4 - 1/2*a^3 - 1/2*a', '1/26*a^14 - 2/13*a^10 + 7/26*a^8 + 4/13*a^6 - 1/2*a^5 - 1/26*a^4 - 1/2*a^3 - 1/2', '1/338*a^15 + 3/338*a^13 + 57/338*a^11 - 28/169*a^9 - 41/169*a^7 - 1/2*a^6 - 9/26*a^5 + 1/26*a^3', '1/1626794*a^16 + 6781/813397*a^14 + 25719/1626794*a^12 - 49831/813397*a^10 - 446775/1626794*a^8 - 1/2*a^7 - 15577/125138*a^6 - 1/2*a^5 - 15584/62569*a^4 - 1/2*a^3 + 668/4813*a^2 + 2747/9626', '1/1626794*a^17 - 877/1626794*a^15 - 8799/813397*a^13 - 54644/813397*a^11 + 361809/1626794*a^9 + 84050/813397*a^7 - 1/2*a^6 - 26355/125138*a^5 - 1/2*a^4 - 29820/62569*a^3 - 1/2*a^2 + 2747/9626*a']}
Number field data - 18.18.45459928664503948293335446409613.1