-
nf_fields • Show schema
{'class_group': [2], 'class_number': 2, 'cm': False, 'coeffs': [1, -12, -59, 80, -65, 3, -11, -52, 30, -20, 11, -2, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 1240804736328125, 'disc_rad': 355, 'disc_sign': 1, 'frobs': [[2, [[12, 1]]], [3, [[12, 1]]], [5, [0]], [7, [[8, 1], [2, 2]]], [11, [[3, 2], [2, 2], [1, 2]]], [13, [[4, 3]]], [17, [[4, 3]]], [19, [[4, 1], [2, 3], [1, 2]]], [23, [[4, 3]]], [29, [[4, 2], [1, 4]]], [31, [[3, 2], [2, 2], [1, 2]]], [37, [[4, 3]]], [41, [[4, 1], [3, 2], [2, 1]]], [43, [[12, 1]]], [47, [[4, 3]]], [53, [[8, 1], [2, 2]]], [59, [[6, 1], [4, 1], [1, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [2112, 1728], 'galois_label': '12T237', 'galt': 237, 'grd': 106.94642350747239, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '12.4.1240804736328125.1', 'local_algs': ['5.1.12.11a1.1', '71.2.1.0a1.1', '71.1.2.1a1.1', '71.1.4.3a1.2', '71.4.1.0a1.1'], 'monogenic': 0, 'narrow_class_group': [2, 2], 'narrow_class_number': 4, 'num_ram': 2, 'r2': 4, 'ramps': [5, 71], 'rd': 18.105420684111436, 'regulator': {'__RealLiteral__': 0, 'data': '418.7100827562533', 'prec': 57}, 'subfield_mults': [1, 1], 'subfields': ['-1.-1.1', '-1.3.0.0.0.-2.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{25656}{684991} a^{11} - \\frac{37074}{684991} a^{10} + \\frac{247224}{684991} a^{9} - \\frac{338756}{684991} a^{8} + \\frac{431102}{684991} a^{7} - \\frac{810043}{684991} a^{6} - \\frac{1098761}{684991} a^{5} - \\frac{133754}{684991} a^{4} - \\frac{1408984}{684991} a^{3} + \\frac{709873}{684991} a^{2} + \\frac{154912}{684991} a - \\frac{435922}{684991} \\)', '\\( -\\frac{229531150}{1643293409} a^{11} + \\frac{445927331}{1643293409} a^{10} - \\frac{2518980862}{1643293409} a^{9} + \\frac{4496530814}{1643293409} a^{8} - \\frac{6850967970}{1643293409} a^{7} + \\frac{12066409011}{1643293409} a^{6} + \\frac{2417793016}{1643293409} a^{5} + \\frac{810537515}{1643293409} a^{4} + \\frac{14351519058}{1643293409} a^{3} - \\frac{18127837180}{1643293409} a^{2} + \\frac{13434140776}{1643293409} a + \\frac{954224023}{1643293409} \\)', '\\( -\\frac{178772022}{1643293409} a^{11} + \\frac{334872992}{1643293409} a^{10} - \\frac{1946166543}{1643293409} a^{9} + \\frac{3374360168}{1643293409} a^{8} - \\frac{5184636021}{1643293409} a^{7} + \\frac{9138999755}{1643293409} a^{6} + \\frac{2486912517}{1643293409} a^{5} + \\frac{1110552246}{1643293409} a^{4} + \\frac{11993120411}{1643293409} a^{3} - \\frac{13644100668}{1643293409} a^{2} + \\frac{8604427081}{1643293409} a + \\frac{294079265}{1643293409} \\)', '\\( -\\frac{399433444}{1643293409} a^{11} + \\frac{753424731}{1643293409} a^{10} - \\frac{4336973777}{1643293409} a^{9} + \\frac{7532614082}{1643293409} a^{8} - \\frac{11320771534}{1643293409} a^{7} + \\frac{19674479456}{1643293409} a^{6} + \\frac{6596124137}{1643293409} a^{5} - \\frac{284587066}{1643293409} a^{4} + \\frac{27105375043}{1643293409} a^{3} - \\frac{28686365745}{1643293409} a^{2} + \\frac{21647300486}{1643293409} a + \\frac{6832206875}{1643293409} \\)', '\\( \\frac{13134969}{1643293409} a^{11} - \\frac{5861788}{1643293409} a^{10} + \\frac{94092186}{1643293409} a^{9} - \\frac{34966530}{1643293409} a^{8} - \\frac{130789211}{1643293409} a^{7} + \\frac{107049634}{1643293409} a^{6} - \\frac{1499130965}{1643293409} a^{5} + \\frac{568005692}{1643293409} a^{4} - \\frac{234654820}{1643293409} a^{3} + \\frac{108197074}{1643293409} a^{2} + \\frac{1800149777}{1643293409} a - \\frac{1872824559}{1643293409} \\)', '\\( \\frac{46625576}{1643293409} a^{11} - \\frac{102719277}{1643293409} a^{10} + \\frac{533576964}{1643293409} a^{9} - \\frac{1041933943}{1643293409} a^{8} + \\frac{1553350177}{1643293409} a^{7} - \\frac{2755301222}{1643293409} a^{6} - \\frac{165497092}{1643293409} a^{5} - \\frac{76210718}{1643293409} a^{4} - \\frac{2271827167}{1643293409} a^{3} + \\frac{3718560409}{1643293409} a^{2} - \\frac{2235931584}{1643293409} a + \\frac{312184338}{1643293409} \\)', '\\( -\\frac{132146446}{1643293409} a^{11} + \\frac{232153715}{1643293409} a^{10} - \\frac{1412589579}{1643293409} a^{9} + \\frac{2332426225}{1643293409} a^{8} - \\frac{3631285844}{1643293409} a^{7} + \\frac{6383698533}{1643293409} a^{6} + \\frac{2321415425}{1643293409} a^{5} + \\frac{1034341528}{1643293409} a^{4} + \\frac{9721293244}{1643293409} a^{3} - \\frac{9925540259}{1643293409} a^{2} + \\frac{6368495497}{1643293409} a + \\frac{2249557012}{1643293409} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', '1/1643293409*a^11 - 558653895/1643293409*a^10 + 788035058/1643293409*a^9 + 158917792/1643293409*a^8 + 692978894/1643293409*a^7 - 262585762/1643293409*a^6 + 305038149/1643293409*a^5 - 328767758/1643293409*a^4 + 223547089/1643293409*a^3 - 170223947/1643293409*a^2 + 177357141/1643293409*a - 258156454/1643293409']}
Number field data - 12.4.1240804736328125.1