-
nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': False, 'coeffs': [20785248, 0, -13856832, 0, 3464208, 0, -769824, 0, 256608, 0, -38880, 0, 7452, 0, -1080, 0, 162, 0, -12, 0, 1], 'conductor': 0, 'degree': 20, 'dirichlet_group': [], 'disc_abs': 5016449852600330836716407488512, 'disc_rad': 66, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[20, 1]]], [7, [[10, 2]]], [11, [0]], [13, [[10, 2]]], [17, [[10, 1], [5, 2]]], [19, [[10, 1], [1, 10]]], [23, [[4, 5]]], [29, [[10, 2]]], [31, [[20, 1]]], [37, [[20, 1]]], [41, [[10, 1], [5, 2]]], [43, [[10, 1], [5, 2]]], [47, [[20, 1]]], [53, [[20, 1]]], [59, [[10, 1], [2, 5]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [550, 100, 180], 'galois_label': '20T53', 'galt': 53, 'grd': 100.84317994603103, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '20.0.5016449852600330836716407488512.2', 'local_algs': ['m2.4.5.55', '3.10.5.1', '3.10.5.1', '11.10.9.4', '11.10.0.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 10, 'ramps': [2, 3, 11], 'rd': 34.2783432843, 'regulator': {'__RealLiteral__': 0, 'data': '3611756.8811914893', 'prec': 60}, 'subfield_mults': [1, 1, 1], 'subfields': ['2.0.1', '198.0.12.0.1', '1.-2.-1.2.2.0.-3.2.1.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1170421}{6337718462448} a^{18} - \\frac{1772507}{1056286410408} a^{16} + \\frac{1516919}{58682578356} a^{14} - \\frac{837701}{6520286484} a^{12} + \\frac{381581}{362238138} a^{10} - \\frac{23816237}{6520286484} a^{8} + \\frac{1209431}{40248682} a^{6} - \\frac{390416}{60373023} a^{4} + \\frac{7759340}{20124341} a^{2} - \\frac{14008650}{20124341} \\)', '\\( \\frac{2897}{352095470136} a^{18} - \\frac{701327}{2112572820816} a^{16} + \\frac{57431}{14670644589} a^{14} - \\frac{546}{20124341} a^{12} + \\frac{1315649}{19560859452} a^{10} + \\frac{1363912}{1630071621} a^{8} - \\frac{3257437}{543357207} a^{6} + \\frac{943373}{181119069} a^{4} - \\frac{5072746}{60373023} a^{2} + \\frac{16876614}{20124341} \\)', '\\( \\frac{2651761}{6337718462448} a^{18} - \\frac{2145929}{528143205204} a^{16} + \\frac{3258913}{58682578356} a^{14} - \\frac{32631263}{117365156712} a^{12} + \\frac{37114423}{19560859452} a^{10} - \\frac{5490467}{724476276} a^{8} + \\frac{12071455}{181119069} a^{6} - \\frac{9993563}{120746046} a^{4} + \\frac{48034355}{60373023} a^{2} - \\frac{54921555}{20124341} \\)', '\\( \\frac{292961}{1584429615612} a^{18} - \\frac{1534481}{704190940272} a^{16} + \\frac{4773331}{176047735068} a^{14} - \\frac{18492941}{117365156712} a^{12} + \\frac{16408087}{19560859452} a^{10} - \\frac{22545095}{6520286484} a^{8} + \\frac{13291519}{543357207} a^{6} - \\frac{9643915}{181119069} a^{4} + \\frac{16267846}{60373023} a^{2} - \\frac{25602799}{20124341} \\)', '\\( \\frac{11924231}{3168859231224} a^{19} + \\frac{13714555}{3168859231224} a^{18} - \\frac{80358221}{2112572820816} a^{17} - \\frac{10177847}{264071602602} a^{16} + \\frac{15444581}{29341289178} a^{15} + \\frac{32882039}{58682578356} a^{14} - \\frac{341412655}{117365156712} a^{13} - \\frac{83347087}{29341289178} a^{12} + \\frac{99659131}{4890214863} a^{11} + \\frac{437521531}{19560859452} a^{10} - \\frac{200569853}{2173428828} a^{9} - \\frac{177769567}{1630071621} a^{8} + \\frac{381527420}{543357207} a^{7} + \\frac{17054234}{20124341} a^{6} - \\frac{222740321}{181119069} a^{5} - \\frac{403171289}{362238138} a^{4} + \\frac{516351163}{60373023} a^{3} + \\frac{225122995}{20124341} a^{2} - \\frac{556475852}{20124341} a - \\frac{877378472}{20124341} \\)', '\\( \\frac{9035}{7710119784} a^{19} + \\frac{4655}{2891294919} a^{18} - \\frac{49369}{3855059892} a^{17} - \\frac{14383}{963764973} a^{16} + \\frac{240379}{1285019964} a^{15} + \\frac{136001}{642509982} a^{14} - \\frac{263279}{214169994} a^{13} - \\frac{115612}{107084997} a^{12} + \\frac{336983}{35694999} a^{11} + \\frac{285257}{35694999} a^{10} - \\frac{569933}{11898333} a^{9} - \\frac{405416}{11898333} a^{8} + \\frac{412085}{1322037} a^{7} + \\frac{1111264}{3966111} a^{6} - \\frac{325238}{440679} a^{5} - \\frac{257752}{1322037} a^{4} + \\frac{1970452}{440679} a^{3} + \\frac{1379048}{440679} a^{2} - \\frac{2121812}{146893} a - \\frac{2653245}{146893} \\)', '\\( \\frac{10555555}{2112572820816} a^{19} + \\frac{73029883}{6337718462448} a^{18} - \\frac{29268631}{528143205204} a^{17} - \\frac{15316421}{78243437808} a^{16} + \\frac{54499831}{88023867534} a^{15} + \\frac{894765527}{352095470136} a^{14} - \\frac{22842413}{9780429726} a^{13} - \\frac{2348495621}{117365156712} a^{12} + \\frac{12168541}{6520286484} a^{11} + \\frac{128708215}{1086714414} a^{10} + \\frac{541179497}{6520286484} a^{9} - \\frac{182015515}{362238138} a^{8} - \\frac{403265861}{1086714414} a^{7} + \\frac{2358955697}{1086714414} a^{6} + \\frac{689055479}{181119069} a^{5} - \\frac{911972989}{181119069} a^{4} - \\frac{895768796}{60373023} a^{3} - \\frac{23400675}{20124341} a^{2} + \\frac{377781902}{20124341} a + \\frac{319222258}{20124341} \\)', '\\( \\frac{2501321}{1584429615612} a^{19} - \\frac{5096053}{2112572820816} a^{18} - \\frac{26524883}{2112572820816} a^{17} + \\frac{5818037}{528143205204} a^{16} + \\frac{69391181}{352095470136} a^{15} - \\frac{76215623}{352095470136} a^{14} - \\frac{87922853}{117365156712} a^{13} + \\frac{16062701}{117365156712} a^{12} + \\frac{20193131}{3260143242} a^{11} - \\frac{99818887}{19560859452} a^{10} - \\frac{29525137}{2173428828} a^{9} + \\frac{9286303}{1630071621} a^{8} + \\frac{65989351}{362238138} a^{7} - \\frac{172440098}{543357207} a^{6} + \\frac{73647161}{181119069} a^{5} - \\frac{12708156}{20124341} a^{4} + \\frac{161999050}{60373023} a^{3} - \\frac{152430737}{20124341} a^{2} + \\frac{51806696}{20124341} a + \\frac{127145547}{20124341} \\)', '\\( \\frac{15972497}{6337718462448} a^{19} + \\frac{1384807}{352095470136} a^{18} - \\frac{3804221}{176047735068} a^{17} - \\frac{175709}{4890214863} a^{16} + \\frac{14131075}{44011933767} a^{15} + \\frac{172375715}{352095470136} a^{14} - \\frac{90754085}{58682578356} a^{13} - \\frac{2416511}{1086714414} a^{12} + \\frac{60926150}{4890214863} a^{11} + \\frac{101840021}{6520286484} a^{10} - \\frac{63344653}{1086714414} a^{9} - \\frac{42454625}{724476276} a^{8} + \\frac{86500577}{181119069} a^{7} + \\frac{330301006}{543357207} a^{6} - \\frac{92219099}{120746046} a^{5} - \\frac{26422856}{60373023} a^{4} + \\frac{148516295}{20124341} a^{3} + \\frac{485293711}{60373023} a^{2} - \\frac{456682320}{20124341} a - \\frac{658756728}{20124341} \\)'], 'used_grh': True, 'zk': ['1', 'a', '1/3*a^2', '1/3*a^3', '1/18*a^4', '1/18*a^5', '1/54*a^6', '1/54*a^7', '1/324*a^8', '1/324*a^9', '1/972*a^10', '1/972*a^11', '1/5832*a^12', '1/5832*a^13', '1/17496*a^14', '1/17496*a^15', '1/104976*a^16', '1/104976*a^17', '1/6337718462448*a^18 + 837739/528143205204*a^16 - 1251545/44011933767*a^14 + 284801/19560859452*a^12 + 203587/9780429726*a^10 - 544400/543357207*a^8 - 7047079/1086714414*a^6 + 5489405/362238138*a^4 + 970885/60373023*a^2 - 4788209/20124341', '1/6337718462448*a^19 + 837739/528143205204*a^17 - 1251545/44011933767*a^15 + 284801/19560859452*a^13 + 203587/9780429726*a^11 - 544400/543357207*a^9 - 7047079/1086714414*a^7 + 5489405/362238138*a^5 + 970885/60373023*a^3 - 4788209/20124341*a']}
Number field data - 20.0.5016449852600330836716407488512.2