-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [1, 5, 10, -25, -35, 92, 65, -275, 50, 375, -261, -285, 535, -295, -5, 48, 45, -75, 40, -10, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 48883259296417236328125, 'disc_rad': 15, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [20, 54], 'galois_label': '20T6', 'galt': 6, 'grd': 15.211433151416195, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.0.48883259296417236328125.1', 'local_algs': ['3.4.1.0a1.1', '3.4.2.4a1.2', '3.4.2.4a1.2', '5.1.20.27a4.1'], 'maximal_cm_subfield': [1, -1, 1, -1, 1], 'maxp': 5, 'monogenic': 0, 'narrow_class_group': [], 'narrow_class_number': 1, 'num_ram': 2, 'r2': 10, 'ramps': [3, 5], 'rd': 13.6288122183, 'regulator': {'__RealLiteral__': 0, 'data': '6025.48578502', 'prec': 44}, 'subfield_mults': [1, 1, 1, 1], 'subfields': ['-1.-1.1', '1.-1.1.-1.1', '-3.0.-5.0.0.1', '-1.0.0.-5.-10.9.10.-5.0.0.1'], 'torsion_order': 10, 'unit_signature_rank': 0, 'used_grh': False} -
nf_fields_extra • Show schema
{'dirichlet_group': [], 'frobs': [[2, [[20, 1]]], [3, [0]], [5, [0]], [7, [[4, 5]]], [11, [[2, 8], [1, 4]]], [13, [[4, 5]]], [17, [[20, 1]]], [19, [[10, 2]]], [23, [[20, 1]]], [29, [[2, 10]]], [31, [[5, 4]]], [37, [[4, 5]]], [41, [[2, 8], [1, 4]]], [43, [[4, 5]]], [47, [[20, 1]]], [53, [[20, 1]]], [59, [[2, 10]]]], 'label': '20.0.48883259296417236328125.1', 'res': {'sib': ['1,0,0,0,0,3,0,0,0,0,-31,0,0,0,0,-3,0,0,0,0,1']}, 'torsion_gen': '\\( \\frac{5327}{7209} a^{19} - \\frac{55546}{7209} a^{18} + \\frac{2947}{89} a^{17} - \\frac{172022}{2403} a^{16} + \\frac{167444}{2403} a^{15} - \\frac{214}{267} a^{14} - \\frac{35932}{7209} a^{13} - \\frac{1505059}{7209} a^{12} + \\frac{44022}{89} a^{11} - \\frac{1111933}{2403} a^{10} + \\frac{111463}{2403} a^{9} + \\frac{209786}{801} a^{8} - \\frac{861800}{7209} a^{7} - \\frac{877220}{7209} a^{6} + \\frac{84553}{801} a^{5} + \\frac{76381}{7209} a^{4} - \\frac{208997}{7209} a^{3} - \\frac{2482}{801} a^{2} + \\frac{44504}{7209} a + \\frac{7502}{7209} \\)', 'units': ['\\( \\frac{3308}{7209} a^{19} - \\frac{31426}{7209} a^{18} + \\frac{41272}{2403} a^{17} - \\frac{9299}{267} a^{16} + \\frac{9482}{267} a^{15} - \\frac{34699}{2403} a^{14} + \\frac{158495}{7209} a^{13} - \\frac{792883}{7209} a^{12} + \\frac{546023}{2403} a^{11} - \\frac{191972}{801} a^{10} + \\frac{91814}{801} a^{9} + \\frac{22294}{2403} a^{8} - \\frac{185639}{7209} a^{7} - \\frac{80168}{7209} a^{6} + \\frac{56176}{2403} a^{5} - \\frac{84791}{7209} a^{4} + \\frac{31261}{7209} a^{3} - \\frac{7271}{2403} a^{2} + \\frac{6554}{7209} a + \\frac{3797}{7209} \\)', '\\( \\frac{3317}{7209} a^{19} - \\frac{32980}{7209} a^{18} + \\frac{44515}{2403} a^{17} - \\frac{29434}{801} a^{16} + \\frac{7802}{267} a^{15} + \\frac{26504}{2403} a^{14} - \\frac{53725}{7209} a^{13} - \\frac{816208}{7209} a^{12} + \\frac{605195}{2403} a^{11} - \\frac{159166}{801} a^{10} - \\frac{38449}{801} a^{9} + \\frac{485512}{2403} a^{8} - \\frac{725504}{7209} a^{7} - \\frac{381545}{7209} a^{6} + \\frac{145204}{2403} a^{5} - \\frac{17705}{7209} a^{4} - \\frac{101852}{7209} a^{3} + \\frac{17416}{2403} a^{2} - \\frac{5587}{7209} a - \\frac{1294}{7209} \\)', '\\( \\frac{3311}{7209} a^{19} - \\frac{28384}{7209} a^{18} + \\frac{30338}{2403} a^{17} - \\frac{36634}{2403} a^{16} - \\frac{13241}{2403} a^{15} + \\frac{52897}{2403} a^{14} + \\frac{173729}{7209} a^{13} - \\frac{744232}{7209} a^{12} + \\frac{227458}{2403} a^{11} + \\frac{82204}{2403} a^{10} - \\frac{292078}{2403} a^{9} + \\frac{76664}{2403} a^{8} + \\frac{545677}{7209} a^{7} - \\frac{283511}{7209} a^{6} - \\frac{52009}{2403} a^{5} + \\frac{102844}{7209} a^{4} + \\frac{45808}{7209} a^{3} - \\frac{6340}{2403} a^{2} - \\frac{24460}{7209} a - \\frac{5020}{7209} \\)', '\\( \\frac{734}{7209} a^{19} - \\frac{15250}{7209} a^{18} + \\frac{33233}{2403} a^{17} - \\frac{100390}{2403} a^{16} + \\frac{140506}{2403} a^{15} - \\frac{41624}{2403} a^{14} - \\frac{210286}{7209} a^{13} - \\frac{482941}{7209} a^{12} + \\frac{709051}{2403} a^{11} - \\frac{918974}{2403} a^{10} + \\frac{323846}{2403} a^{9} + \\frac{438170}{2403} a^{8} - \\frac{1214027}{7209} a^{7} - \\frac{321989}{7209} a^{6} + \\frac{235424}{2403} a^{5} - \\frac{135230}{7209} a^{4} - \\frac{173138}{7209} a^{3} + \\frac{20741}{2403} a^{2} + \\frac{38852}{7209} a - \\frac{400}{7209} \\)', '\\( \\frac{287}{801} a^{19} - \\frac{2237}{801} a^{18} + \\frac{18491}{2403} a^{17} - \\frac{14879}{2403} a^{16} - \\frac{17956}{2403} a^{15} + \\frac{16063}{2403} a^{14} + \\frac{72746}{2403} a^{13} - \\frac{139391}{2403} a^{12} + \\frac{55543}{2403} a^{11} + \\frac{95177}{2403} a^{10} - \\frac{73403}{2403} a^{9} - \\frac{101644}{2403} a^{8} + \\frac{81406}{2403} a^{7} + \\frac{82943}{2403} a^{6} - \\frac{62986}{2403} a^{5} - \\frac{31046}{2403} a^{4} + \\frac{31238}{2403} a^{3} + \\frac{7889}{2403} a^{2} - \\frac{13745}{2403} a - \\frac{3235}{2403} \\)', '\\( \\frac{3673}{7209} a^{19} - \\frac{31022}{7209} a^{18} + \\frac{32500}{2403} a^{17} - \\frac{37661}{2403} a^{16} - \\frac{16201}{2403} a^{15} + \\frac{52670}{2403} a^{14} + \\frac{212830}{7209} a^{13} - \\frac{783812}{7209} a^{12} + \\frac{219113}{2403} a^{11} + \\frac{101981}{2403} a^{10} - \\frac{285782}{2403} a^{9} + \\frac{43894}{2403} a^{8} + \\frac{525035}{7209} a^{7} - \\frac{93808}{7209} a^{6} - \\frac{94829}{2403} a^{5} + \\frac{98351}{7209} a^{4} + \\frac{89765}{7209} a^{3} - \\frac{11420}{2403} a^{2} - \\frac{38072}{7209} a - \\frac{1205}{7209} \\)', '\\( \\frac{3602}{7209} a^{19} - \\frac{27277}{7209} a^{18} + \\frac{21631}{2403} a^{17} + \\frac{289}{267} a^{16} - \\frac{28949}{801} a^{15} + \\frac{94442}{2403} a^{14} + \\frac{287858}{7209} a^{13} - \\frac{666613}{7209} a^{12} - \\frac{71320}{2403} a^{11} + \\frac{188665}{801} a^{10} - \\frac{185945}{801} a^{9} - \\frac{57887}{2403} a^{8} + \\frac{1030840}{7209} a^{7} + \\frac{29767}{7209} a^{6} - \\frac{192050}{2403} a^{5} + \\frac{109792}{7209} a^{4} + \\frac{153373}{7209} a^{3} - \\frac{7169}{2403} a^{2} - \\frac{72856}{7209} a - \\frac{12277}{7209} \\)', '\\( \\frac{7834}{7209} a^{19} - \\frac{67748}{7209} a^{18} + \\frac{24913}{801} a^{17} - \\frac{103612}{2403} a^{16} + \\frac{16309}{2403} a^{15} + \\frac{20158}{801} a^{14} + \\frac{482479}{7209} a^{13} - \\frac{1712678}{7209} a^{12} + \\frac{208826}{801} a^{11} - \\frac{126611}{2403} a^{10} - \\frac{272140}{2403} a^{9} - \\frac{198}{89} a^{8} + \\frac{899525}{7209} a^{7} - \\frac{182554}{7209} a^{6} - \\frac{43720}{801} a^{5} + \\frac{68219}{7209} a^{4} + \\frac{181379}{7209} a^{3} - \\frac{5855}{801} a^{2} - \\frac{44528}{7209} a - \\frac{9260}{7209} \\)', '\\( \\frac{5155}{7209} a^{19} - \\frac{44300}{7209} a^{18} + \\frac{16267}{801} a^{17} - \\frac{67228}{2403} a^{16} + \\frac{3928}{2403} a^{15} + \\frac{22630}{801} a^{14} + \\frac{182593}{7209} a^{13} - \\frac{1097147}{7209} a^{12} + \\frac{148607}{801} a^{11} - \\frac{44537}{2403} a^{10} - \\frac{390520}{2403} a^{9} + \\frac{29491}{267} a^{8} + \\frac{401561}{7209} a^{7} - \\frac{580717}{7209} a^{6} - \\frac{772}{801} a^{5} + \\frac{236093}{7209} a^{4} - \\frac{46225}{7209} a^{3} - \\frac{4472}{801} a^{2} + \\frac{3391}{7209} a + \\frac{1705}{7209} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', '1/3*a^10 + 1/3*a^9 - 1/3*a^8 + 1/3*a^7 + 1/3*a^6 + 1/3*a^5 - 1/3*a + 1/3', '1/3*a^11 + 1/3*a^9 - 1/3*a^8 - 1/3*a^5 - 1/3*a^2 - 1/3*a - 1/3', '1/3*a^12 + 1/3*a^9 + 1/3*a^8 - 1/3*a^7 + 1/3*a^6 - 1/3*a^5 - 1/3*a^3 - 1/3*a^2 - 1/3', '1/3*a^13 + 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/3*a^3 - 1/3', '1/3*a^14 + 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^4 - 1/3*a', '1/3*a^15 + 1/3*a^8 - 1/3*a^7 - 1/3*a^6 - 1/3*a^5 - 1/3*a^2', '1/9*a^16 + 1/9*a^15 - 1/9*a^13 - 1/9*a^12 - 1/9*a^10 - 4/9*a^9 - 1/3*a^8 - 2/9*a^7 - 2/9*a^6 - 2/9*a^4 - 2/9*a^3 + 1/3*a^2 + 1/9*a - 2/9', '1/27*a^17 - 1/27*a^16 + 1/27*a^15 - 4/27*a^14 + 1/27*a^13 + 2/27*a^12 - 1/27*a^11 + 1/27*a^10 - 10/27*a^9 - 5/27*a^8 - 10/27*a^7 - 2/27*a^6 + 1/27*a^5 + 5/27*a^4 - 2/27*a^3 + 1/27*a^2 - 13/27*a - 2/27', '1/27*a^18 - 1/9*a^15 - 1/9*a^14 + 1/9*a^13 + 1/27*a^12 - 2/9*a^9 + 1/9*a^8 - 1/9*a^7 + 8/27*a^6 - 4/9*a^5 + 1/9*a^4 - 1/27*a^3 - 4/9*a^2 + 1/9*a + 7/27', '1/7209*a^19 + 124/7209*a^18 + 34/2403*a^17 - 8/2403*a^16 + 11/2403*a^15 - 379/2403*a^14 - 173/7209*a^13 + 553/7209*a^12 + 137/2403*a^11 + 374/2403*a^10 - 701/2403*a^9 - 626/2403*a^8 - 88/7209*a^7 - 52/7209*a^6 + 814/2403*a^5 + 2915/7209*a^4 + 2891/7209*a^3 - 728/2403*a^2 + 520/7209*a + 1600/7209']}
Number field data - 20.0.48883259296417236328125.1