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nf_fields • Show schema
{'class_group': [3], 'class_number': 3, 'cm': False, 'coeffs': [21952, 0, 0, -6048, 0, 0, 6720, 0, 0, -1672, 0, 0, 360, 0, 0, -30, 0, 0, 1], 'conductor': 0, 'degree': 18, 'dirichlet_group': [], 'disc_abs': 520986863358984384396363313152, 'disc_rad': 42, 'disc_sign': -1, 'frobs': [[2, [0]], [3, [0]], [5, [[6, 3]]], [7, [0]], [11, [[6, 3]]], [13, [[6, 2], [3, 2]]], [17, [[6, 3]]], [19, [[6, 1], [3, 1], [2, 3], [1, 3]]], [23, [[6, 3]]], [29, [[2, 9]]], [31, [[6, 2], [3, 2]]], [37, [[3, 6]]], [41, [[6, 3]]], [43, [[3, 6]]], [47, [[6, 3]]], [53, [[6, 3]]], [59, [[6, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [72, 222, 90], 'galois_label': '18T46', 'galt': 46, 'grd': 76.8571500447917, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 1, 'label': '18.0.520986863358984384396363313152.1', 'local_algs': ['2.18.12.1', 'm3.18.1.37', '7.3.2.3', '7.3.0.1', '7.6.5.6', '7.6.3.2'], 'minimal_sibling': [4032, 0, 0, 3024, 0, 0, 564, 0, 0, -18, 0, 0, 1], 'monogenic': 0, 'num_ram': 3, 'r2': 9, 'ramps': [2, 3, 7], 'rd': 44.7646116017, 'regulator': {'__RealLiteral__': 0, 'data': '36855368.88515014', 'prec': 57}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['1.-1.1', '-2.-6.0.1', '7.-21.30.-19.12.-3.1', '63.0.0.-3.0.0.1'], 'torsion_gen': '\\( -\\frac{1}{15366} a^{15} + \\frac{281}{122928} a^{12} - \\frac{250}{7683} a^{9} + \\frac{1477}{7683} a^{6} - \\frac{4207}{7683} a^{3} + \\frac{9539}{7683} \\)', 'torsion_order': 6, 'units': ['\\( \\frac{3817}{36140832} a^{17} + \\frac{3127}{10325952} a^{16} - \\frac{977}{5162976} a^{15} - \\frac{131191}{36140832} a^{14} - \\frac{22417}{2581488} a^{13} + \\frac{7859}{1290744} a^{12} + \\frac{936323}{18070416} a^{11} + \\frac{247459}{2581488} a^{10} - \\frac{52099}{645372} a^{9} - \\frac{1526593}{4517604} a^{8} - \\frac{215261}{645372} a^{7} + \\frac{150607}{322686} a^{6} + \\frac{867379}{645372} a^{5} + \\frac{99503}{92196} a^{4} - \\frac{93565}{46098} a^{3} - \\frac{780293}{322686} a^{2} + \\frac{29335}{23049} a + \\frac{93752}{23049} \\)', '\\( \\frac{3817}{36140832} a^{17} + \\frac{3127}{10325952} a^{16} - \\frac{977}{5162976} a^{15} - \\frac{131191}{36140832} a^{14} - \\frac{22417}{2581488} a^{13} + \\frac{7859}{1290744} a^{12} + \\frac{936323}{18070416} a^{11} + \\frac{247459}{2581488} a^{10} - \\frac{52099}{645372} a^{9} - \\frac{1526593}{4517604} a^{8} - \\frac{215261}{645372} a^{7} + \\frac{150607}{322686} a^{6} + \\frac{867379}{645372} a^{5} + \\frac{99503}{92196} a^{4} - \\frac{93565}{46098} a^{3} - \\frac{780293}{322686} a^{2} + \\frac{29335}{23049} a + \\frac{70703}{23049} \\)', '\\( \\frac{547}{9035208} a^{17} - \\frac{307}{2581488} a^{15} - \\frac{28823}{18070416} a^{14} + \\frac{9823}{2581488} a^{12} + \\frac{32521}{2258802} a^{11} - \\frac{58823}{1290744} a^{9} - \\frac{40823}{9035208} a^{8} + \\frac{28829}{161343} a^{6} - \\frac{24671}{645372} a^{5} - \\frac{6737}{23049} a^{3} + \\frac{92485}{322686} a^{2} + \\frac{25175}{23049} \\)', '\\( \\frac{215}{36140832} a^{17} - \\frac{439}{5162976} a^{15} - \\frac{10433}{36140832} a^{14} + \\frac{5309}{2581488} a^{12} + \\frac{71677}{18070416} a^{11} - \\frac{19021}{1290744} a^{9} - \\frac{85789}{9035208} a^{8} - \\frac{31895}{645372} a^{6} - \\frac{25057}{161343} a^{5} + \\frac{1277}{23049} a^{3} - \\frac{10880}{161343} a^{2} + \\frac{4348}{23049} \\)', '\\( \\frac{1973}{36140832} a^{17} - \\frac{25}{737568} a^{15} - \\frac{47213}{36140832} a^{14} + \\frac{2257}{1290744} a^{12} + \\frac{188491}{18070416} a^{11} - \\frac{2843}{92196} a^{9} + \\frac{22483}{4517604} a^{8} + \\frac{147211}{645372} a^{6} + \\frac{75557}{645372} a^{5} - \\frac{8014}{23049} a^{3} + \\frac{114245}{322686} a^{2} + \\frac{20827}{23049} \\)', '\\( \\frac{1}{44128} a^{15} - \\frac{65}{66192} a^{12} + \\frac{125}{11032} a^{9} - \\frac{123}{5516} a^{6} + \\frac{53}{1182} a^{3} + \\frac{96}{197} \\)', '\\( \\frac{44801}{72281664} a^{17} + \\frac{83}{61464} a^{16} - \\frac{179}{107562} a^{15} - \\frac{388847}{18070416} a^{14} - \\frac{9977}{286832} a^{13} + \\frac{23869}{430248} a^{12} + \\frac{5313293}{18070416} a^{11} + \\frac{18451}{61464} a^{10} - \\frac{304219}{430248} a^{9} - \\frac{1755004}{1129401} a^{8} - \\frac{13007}{215124} a^{7} + \\frac{711797}{215124} a^{6} + \\frac{1741681}{645372} a^{5} + \\frac{3989}{5122} a^{4} - \\frac{33310}{7683} a^{3} - \\frac{692065}{161343} a^{2} + \\frac{30635}{7683} a + \\frac{84778}{7683} \\)', '\\( \\frac{44801}{72281664} a^{17} - \\frac{1619}{1720992} a^{16} + \\frac{2075}{860496} a^{15} - \\frac{388847}{18070416} a^{14} + \\frac{1507}{53781} a^{13} - \\frac{59119}{860496} a^{12} + \\frac{5313293}{18070416} a^{11} - \\frac{130667}{430248} a^{10} + \\frac{151813}{215124} a^{9} - \\frac{1755004}{1129401} a^{8} + \\frac{86665}{107562} a^{7} - \\frac{368413}{215124} a^{6} + \\frac{1741681}{645372} a^{5} + \\frac{4972}{7683} a^{4} + \\frac{66553}{15366} a^{3} - \\frac{692065}{161343} a^{2} + \\frac{14390}{7683} a - \\frac{62186}{7683} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', '1/2*a^3', '1/2*a^4', '1/2*a^5', '1/4*a^6', '1/4*a^7', '1/8*a^8 - 1/4*a^5 - 1/2*a^2', '1/24*a^9 - 1/3', '1/24*a^10 - 1/3*a', '1/48*a^11 - 1/6*a^2', '1/336*a^12 + 1/14*a^6 - 1/6*a^3', '1/672*a^13 - 5/56*a^7 + 1/6*a^4 - 1/2*a', '1/2016*a^14 - 1/2016*a^13 - 1/1008*a^12 - 1/144*a^11 - 1/72*a^10 + 1/72*a^9 - 5/168*a^8 + 5/168*a^7 + 5/84*a^6 - 1/9*a^5 + 1/9*a^4 + 2/9*a^3 - 1/9*a^2 + 5/18*a + 2/9', '1/5162976*a^15 + 1423/2581488*a^12 + 4513/322686*a^9 - 71437/645372*a^6 - 1403/23049*a^3 - 1480/23049', '1/10325952*a^16 + 1423/5162976*a^13 - 35729/2581488*a^10 - 71437/1290744*a^7 + 20243/92196*a^4 + 6203/46098*a', '1/72281664*a^17 - 8821/36140832*a^14 + 1/2016*a^13 + 1/1008*a^12 + 1870/376467*a^11 + 1/72*a^10 - 1/72*a^9 + 404909/9035208*a^8 - 5/168*a^7 - 5/84*a^6 + 61219/645372*a^5 - 1/9*a^4 - 2/9*a^3 - 6627/17927*a^2 - 5/18*a - 2/9']}
Number field data - 18.0.520986863358984384396363313152.1