-
nf_fields • Show schema
{'class_group': [2, 2, 2], 'class_number': 8, 'cm': True, 'coeffs': [14641, 0, -33759, 0, 63200, 0, -29161, 0, 9219, 0, -1741, 0, 240, 0, -19, 0, 1], 'conductor': 420, 'degree': 16, 'dirichlet_group': [1, 83, 71, 13, 211, 281, 29, 223, 97, 293, 167, 169, 239, 307, 377, 379], 'disc_abs': 605165749776000000000000, 'disc_rad': 210, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [0]], [11, [[2, 8]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[2, 8]]], [23, [[4, 4]]], [29, [[2, 8]]], [31, [[2, 8]]], [37, [[4, 4]]], [41, [[2, 8]]], [43, [[4, 4]]], [47, [[4, 4]]], [53, [[4, 4]]], [59, [[2, 8]]]], 'gal_is_abelian': True, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [16, 8, 12, 8], 'galois_label': '16T2', 'galt': 2, 'grd': 30.645530678223075, 'index': 1, 'inessentialp': [], 'is_galois': True, 'is_minimal_sibling': True, 'iso_number': 7, 'label': '16.0.605165749776000000000000.7', 'local_algs': ['2.4.2.8a1.1', '2.4.2.8a1.1', '3.4.2.4a1.2', '3.4.2.4a1.2', '5.2.4.6a1.2', '5.2.4.6a1.2', '7.2.2.2a1.1', '7.2.2.2a1.1', '7.2.2.2a1.1', '7.2.2.2a1.1'], 'maximal_cm_subfield': [14641, 0, -33759, 0, 63200, 0, -29161, 0, 9219, 0, -1741, 0, 240, 0, -19, 0, 1], 'monogenic': 0, 'narrow_class_group': [2, 2, 2], 'narrow_class_number': 8, 'num_ram': 4, 'r2': 8, 'ramps': [2, 3, 5, 7], 'rd': 30.6455306782, 'regulator': {'__RealLiteral__': 0, 'data': '76884.6053994', 'prec': 44}, 'relative_class_number': 4, 'res': {}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['1.0.1', '1.-1.1', '-3.0.1', '-1.-1.1', '5.0.1', '4.-1.1', '-15.0.1', '1.0.-1.0.1', '1.0.3.0.1', '16.0.-7.0.1', '1.1.2.-1.1', '25.0.-5.0.1', '1.8.-7.-2.1', '4.0.1.0.1', '2205.0.-105.0.1', '151.-26.26.-1.1', '245.0.35.0.1', '11.9.-9.-1.1', '1.0.-3.0.8.0.-3.0.1', '22801.0.-7176.0.926.0.-51.0.1', '121.0.279.0.121.0.19.0.1', '60025.0.-8575.0.980.0.-35.0.1', '121.99.180.-59.79.-9.10.-1.1', '-59.216.-126.-238.184.54.-29.-2.1', '841.0.272.0.74.0.13.0.1'], 'torsion_gen': '\\( -\\frac{1913329}{92045183099} a^{15} + \\frac{346706790}{1012497014089} a^{13} - \\frac{4150184540}{1012497014089} a^{11} + \\frac{25395094000}{1012497014089} a^{9} - \\frac{115409043000}{1012497014089} a^{7} + \\frac{202993944499}{1012497014089} a^{5} - \\frac{9911044220}{92045183099} a^{3} - \\frac{1313812737840}{1012497014089} a \\)', 'torsion_order': 12, 'units': ['\\( \\frac{2211}{21019681} a^{14} - \\frac{432308}{231216491} a^{12} + \\frac{4795860}{231216491} a^{10} - \\frac{29346000}{231216491} a^{8} + \\frac{116003123}{231216491} a^{6} - \\frac{234575241}{231216491} a^{4} + \\frac{11452980}{21019681} a^{2} + \\frac{8179387}{21019681} \\)', '\\( \\frac{1913329}{92045183099} a^{15} - \\frac{346706790}{1012497014089} a^{13} + \\frac{4150184540}{1012497014089} a^{11} - \\frac{25395094000}{1012497014089} a^{9} + \\frac{115409043000}{1012497014089} a^{7} - \\frac{202993944499}{1012497014089} a^{5} + \\frac{9911044220}{92045183099} a^{3} + \\frac{1313812737840}{1012497014089} a - 1 \\)', '\\( \\frac{1977105}{25359581599} a^{15} + \\frac{700972489}{11137467154979} a^{14} - \\frac{33840010}{25359581599} a^{13} - \\frac{12232808872}{11137467154979} a^{12} + \\frac{426869315}{25359581599} a^{11} + \\frac{123771447179}{11137467154979} a^{10} - \\frac{2974352111}{25359581599} a^{9} - \\frac{663232557440}{11137467154979} a^{8} + \\frac{16495010200}{25359581599} a^{7} + \\frac{1671303830347}{11137467154979} a^{6} - \\frac{39480061}{19053029} a^{5} + \\frac{31283527881}{1012497014089} a^{4} + \\frac{127569956482}{25359581599} a^{3} - \\frac{20300710112720}{11137467154979} a^{2} - \\frac{392145995}{209583319} a + \\frac{152144831913}{92045183099} \\)', '\\( \\frac{1750368606}{11137467154979} a^{14} - \\frac{22240823625}{11137467154979} a^{12} + \\frac{221921283282}{11137467154979} a^{10} - \\frac{875110320306}{11137467154979} a^{8} + \\frac{2844398064714}{11137467154979} a^{6} - \\frac{58154153858}{1012497014089} a^{4} + \\frac{4372605041031}{11137467154979} a^{2} - \\frac{16751090454}{92045183099} \\)', '\\( \\frac{4816075}{92045183099} a^{15} - \\frac{920857381}{1012497014089} a^{13} + \\frac{10446504500}{1012497014089} a^{11} - \\frac{63922450000}{1012497014089} a^{9} + \\frac{260228515359}{1012497014089} a^{7} - \\frac{510959725825}{1012497014089} a^{5} + \\frac{24947268500}{92045183099} a^{3} - \\frac{608145287463}{1012497014089} a \\)', '\\( \\frac{8554798408}{122512138704769} a^{15} - \\frac{7237445019}{11137467154979} a^{14} + \\frac{78480172205}{122512138704769} a^{13} + \\frac{87580041851}{11137467154979} a^{12} - \\frac{1678433057976}{122512138704769} a^{11} - \\frac{831521155263}{11137467154979} a^{10} + \\frac{23980867099986}{122512138704769} a^{9} + \\frac{2754412221479}{11137467154979} a^{8} - \\frac{125522026428687}{122512138704769} a^{7} - \\frac{6474184370161}{11137467154979} a^{6} + \\frac{3892363270514}{1012497014089} a^{5} - \\frac{1465975132089}{1012497014089} a^{4} - \\frac{578279762728196}{122512138704769} a^{3} + \\frac{24180307477910}{11137467154979} a^{2} + \\frac{1764287706595}{1012497014089} a - \\frac{118312525499}{92045183099} \\)', '\\( \\frac{26282437176}{122512138704769} a^{15} - \\frac{5848164616}{11137467154979} a^{14} - \\frac{459017646465}{122512138704769} a^{13} + \\frac{102997373081}{11137467154979} a^{12} + \\frac{5052555576111}{122512138704769} a^{11} - \\frac{1147114432008}{11137467154979} a^{10} - \\frac{30069572166960}{122512138704769} a^{9} + \\frac{7032881266611}{11137467154979} a^{8} + \\frac{113533319175414}{122512138704769} a^{7} - \\frac{27869094253426}{11137467154979} a^{6} - \\frac{150778307485}{92045183099} a^{5} + \\frac{5190068062805}{1012497014089} a^{4} + \\frac{32131967669810}{122512138704769} a^{3} - \\frac{25599188372831}{11137467154979} a^{2} - \\frac{542992106839}{1012497014089} a + \\frac{70794655219}{92045183099} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', '1/11*a^9 + 1/11*a^7 + 3/11*a^5 - 2/11*a^3 + 4/11*a', '1/11*a^10 + 1/11*a^8 + 3/11*a^6 - 2/11*a^4 + 4/11*a^2', '1/11*a^11 + 2/11*a^7 - 5/11*a^5 - 5/11*a^3 - 4/11*a', '1/11*a^12 + 2/11*a^8 - 5/11*a^6 - 5/11*a^4 - 4/11*a^2', '1/11*a^13 + 4/11*a^7 + 3/11*a', '1/11137467154979*a^14 - 399578710000/11137467154979*a^12 + 124755454976/11137467154979*a^10 + 4072809174926/11137467154979*a^8 - 3879007553519/11137467154979*a^6 + 494941678642/1012497014089*a^4 + 3589762146041/11137467154979*a^2 - 10630726872/92045183099', '1/122512138704769*a^15 + 2637912332267/122512138704769*a^13 + 124755454976/122512138704769*a^11 - 989675895519/122512138704769*a^9 - 7928995609875/122512138704769*a^7 - 356657010010/1012497014089*a^5 + 2577265131952/122512138704769*a^3 - 470856642367/1012497014089*a']}
Number field data - 16.0.605165749776000000000000.7