Formats: - HTML - YAML - JSON - 2026-10-09T02:14:19.441649
  • nf_fields • Show schema
    {'class_group': [2, 2, 492], 'class_number': 1968, 'cm': True, 'coeffs': [15552, 0, 279936, 0, 1586304, 0, 3302208, 0, 2835648, 0, 1203552, 0, 274536, 0, 34488, 0, 2331, 0, 78, 0, 1], 'conductor': 0, 'degree': 20, 'disc_abs': 148184566209122179801351864839045120000, 'disc_rad': 5190, 'disc_sign': 1, 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2700, 600, 400, 400], 'galois_label': '20T157', 'galt': 157, 'grd': 695.5449954322967, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '20.0.148184566209122179801351864839045120000.1', 'local_algs': ['2.1.4.10a1.8', '2.1.16.54o1.297', '3.1.4.3a1.1', '3.4.4.12a1.3', '5.1.1.0a1.1', '5.1.1.0a1.1', '5.2.1.0a1.1', '5.4.1.0a1.1', '5.4.1.0a1.1', '5.2.2.2a1.1', '5.2.2.2a1.1', '173.1.1.0a1.1', '173.1.1.0a1.1', '173.2.1.0a1.1', '173.2.2.2a1.1', '173.4.1.0a1.1', '173.4.1.0a1.1', '173.2.2.2a1.1'], 'maximal_cm_subfield': [15552, 0, 279936, 0, 1586304, 0, 3302208, 0, 2835648, 0, 1203552, 0, 274536, 0, 34488, 0, 2331, 0, 78, 0, 1], 'maxp': 173, 'monogenic': 0, 'narrow_class_group': [2, 2, 492], 'narrow_class_number': 1968, 'num_ram': 4, 'r2': 10, 'ramps': [2, 3, 5, 173], 'rd': 81.0102828742, 'regulator': {'__RealLiteral__': 0, 'data': '255930231.626', 'prec': 40}, 'relative_class_number': 1968, 'subfield_mults': [1, 1, 1], 'subfields': ['-6.0.1', '3.0.6.0.1', '48.216.1.-400.-152.216.118.-32.-24.0.1'], 'torsion_order': 2, 'unit_signature_rank': 0, 'used_grh': True}
  • nf_fields_extra • Show schema
    {'dirichlet_group': [], 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[20, 1]]], [11, [[10, 2]]], [13, [[10, 2]]], [17, [[20, 1]]], [19, [[4, 4], [2, 1], [1, 2]]], [23, [[5, 2], [2, 4], [1, 2]]], [29, [[4, 4], [2, 1], [1, 2]]], [31, [[20, 1]]], [37, [[10, 2]]], [41, [[20, 1]]], [43, [[4, 4], [2, 1], [1, 2]]], [47, [[5, 2], [2, 4], [1, 2]]], [53, [[4, 4], [2, 1], [1, 2]]], [59, [[2, 10]]]], 'label': '20.0.148184566209122179801351864839045120000.1', 'res': {}, 'torsion_gen': '\\( -1 \\)', 'units': ['\\( \\frac{5175623}{87649897680} a^{18} + \\frac{7272657271}{1577698158240} a^{16} + \\frac{36279943849}{262949693040} a^{14} + \\frac{538375006787}{262949693040} a^{12} + \\frac{71830329317}{4382494884} a^{10} + \\frac{2544089074759}{35059959072} a^{8} + \\frac{844170875883}{4869438760} a^{6} + \\frac{2975673860093}{14608316280} a^{4} + \\frac{57163696256}{608679845} a^{2} + \\frac{6486237445}{486943876} \\)', '\\( \\frac{372104101}{6310792632960} a^{18} + \\frac{3570447007}{788849079120} a^{16} + \\frac{92603562751}{701199181440} a^{14} + \\frac{396810431323}{210359754432} a^{12} + \\frac{2504959485061}{175299795360} a^{10} + \\frac{2058804198323}{35059959072} a^{8} + \\frac{1241699182291}{9738877520} a^{6} + \\frac{321408022871}{2434719380} a^{4} + \\frac{12147584677}{243471938} a^{2} + \\frac{11424282723}{2434719380} \\)', '\\( \\frac{1076405}{26854436736} a^{18} + \\frac{207923363}{67136091840} a^{16} + \\frac{1361610431}{14919131520} a^{14} + \\frac{7401798949}{5594674320} a^{12} + \\frac{38166318463}{3729782880} a^{10} + \\frac{4022088665}{93244572} a^{8} + \\frac{3974954885}{41442032} a^{6} + \\frac{15630911167}{155407620} a^{4} + \\frac{945361349}{25901270} a^{2} + \\frac{35507451}{12950635} \\)', '\\( \\frac{164744489}{2103597544320} a^{18} + \\frac{958137197}{157769815824} a^{16} + \\frac{75677938111}{420719508864} a^{14} + \\frac{2761547515753}{1051798772160} a^{12} + \\frac{1197070836667}{58433265120} a^{10} + \\frac{1020732155387}{11686653024} a^{8} + \\frac{5798942623171}{29216632560} a^{6} + \\frac{1616540839147}{7304158140} a^{4} + \\frac{60078973261}{608679845} a^{2} + \\frac{28718392953}{2434719380} \\)', '\\( \\frac{58825673}{1051798772160} a^{18} + \\frac{13709637251}{3155396316480} a^{16} + \\frac{135675213493}{1051798772160} a^{14} + \\frac{1985416849849}{1051798772160} a^{12} + \\frac{32305019885}{2191247442} a^{10} + \\frac{45607999075}{730415814} a^{8} + \\frac{669514232379}{4869438760} a^{6} + \\frac{2015386582969}{14608316280} a^{4} + \\frac{27908284273}{608679845} a^{2} + \\frac{2196797879}{243471938} \\)', '\\( \\frac{958033}{7459565760} a^{18} + \\frac{222805157}{22378697280} a^{16} + \\frac{6595689353}{22378697280} a^{14} + \\frac{32053334591}{7459565760} a^{12} + \\frac{41553912341}{1243260960} a^{10} + \\frac{26313513787}{186489144} a^{8} + \\frac{12034493792}{38851905} a^{6} + \\frac{94816243661}{310815240} a^{4} + \\frac{4447432229}{51802540} a^{2} + \\frac{161054027}{25901270} \\)', '\\( \\frac{319921}{29216632560} a^{18} + \\frac{2549399089}{3155396316480} a^{16} + \\frac{11626104331}{525899386080} a^{14} + \\frac{99393104099}{350599590720} a^{12} + \\frac{78056009723}{43824948840} a^{10} + \\frac{5068149193}{973887752} a^{8} + \\frac{3173917066}{608679845} a^{6} - \\frac{46701650071}{14608316280} a^{4} - \\frac{7384988017}{1217359690} a^{2} - \\frac{844172407}{1217359690} \\)', '\\( \\frac{496403683}{1262158526592} a^{18} + \\frac{96597040007}{3155396316480} a^{16} + \\frac{213132109363}{233733060480} a^{14} + \\frac{7057756673417}{525899386080} a^{12} + \\frac{2063084526543}{19477755040} a^{10} + \\frac{8025922963963}{17529979536} a^{8} + \\frac{2049675094015}{1947775504} a^{6} + \\frac{8513776360613}{7304158140} a^{4} + \\frac{297246889753}{608679845} a^{2} + \\frac{67568682953}{1217359690} \\)', '\\( \\frac{900086149}{6310792632960} a^{18} + \\frac{17557803713}{1577698158240} a^{16} + \\frac{699629298581}{2103597544320} a^{14} + \\frac{1723268350031}{350599590720} a^{12} + \\frac{2276415780551}{58433265120} a^{10} + \\frac{5917364816651}{35059959072} a^{8} + \\frac{11312082370717}{29216632560} a^{6} + \\frac{1560883489439}{3652079070} a^{4} + \\frac{221681635377}{1217359690} a^{2} + \\frac{51086027799}{2434719380} \\)'], 'zk': ['1', 'a', 'a^2', 'a^3', '1/3*a^4', '1/3*a^5', '1/3*a^6', '1/6*a^7 - 1/2*a^3', '1/18*a^8 - 1/6*a^4', '1/18*a^9 - 1/6*a^5', '1/36*a^10 + 1/12*a^6 - 1/6*a^4', '1/36*a^11 - 1/12*a^7 - 1/6*a^5 - 1/2*a^3', '1/864*a^12 - 1/144*a^10 + 5/288*a^8 + 1/24*a^6 + 1/24*a^4 - 1/2*a^2 - 1/4', '1/1728*a^13 + 1/96*a^11 - 11/576*a^9 - 1/36*a^8 + 1/16*a^7 + 1/48*a^5 - 1/12*a^4 - 1/4*a^3 - 1/2*a^2 - 1/8*a', '1/1728*a^14 - 7/576*a^10 - 1/36*a^9 + 5/288*a^8 + 7/48*a^6 - 1/12*a^5 + 1/24*a^4 - 1/2*a^3 + 3/8*a^2 + 1/4', '1/1728*a^15 - 7/576*a^11 + 5/288*a^9 - 1/48*a^7 + 1/24*a^5 - 1/8*a^3 + 1/4*a', '1/51840*a^16 - 1/8640*a^14 - 1/5760*a^12 - 1/72*a^11 + 13/1440*a^10 - 5/288*a^8 - 1/24*a^7 + 1/8*a^6 - 1/12*a^5 - 37/240*a^4 - 1/2*a^3 - 1/10*a^2 - 3/10', '1/51840*a^17 - 1/8640*a^15 - 1/5760*a^13 + 13/1440*a^11 - 5/288*a^9 - 1/24*a^7 - 37/240*a^5 + 2/5*a^3 - 3/10*a', '1/12621585265920*a^18 - 10556197/1577698158240*a^16 - 73008181/1402398362880*a^14 + 374646151/701199181440*a^12 - 649574467/70119918144*a^10 - 180849059/8764989768*a^8 + 1279182043/58433265120*a^6 - 1/6*a^5 - 3865135997/29216632560*a^4 - 730280243/2434719380*a^2 - 1/2*a - 52967555/486943876', '1/12621585265920*a^19 - 10556197/1577698158240*a^17 - 73008181/1402398362880*a^15 - 93421237/2103597544320*a^13 + 63087247/7791102016*a^11 - 107696813/70119918144*a^9 - 1/36*a^8 + 2496541733/58433265120*a^7 - 1/6*a^6 + 65937153/4869438760*a^5 - 1/12*a^4 - 60800199/1217359690*a^3 + 15800859/973887752*a']}