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nf_fields • Show schema
{'class_group': [2, 2], 'class_number': 4, 'cm': True, 'coeffs': [2401, 0, -2352, 0, 1924, 0, -768, 0, 246, 0, 48, 0, 4, 0, 0, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 1495873430980877352960000, 'disc_rad': 30, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[4, 4]]], [11, [[4, 4]]], [13, [[4, 4]]], [17, [[4, 4]]], [19, [[4, 4]]], [23, [[2, 8]]], [29, [[4, 4]]], [31, [[4, 4]]], [37, [[4, 4]]], [41, [[4, 4]]], [43, [[4, 4]]], [47, [[2, 4], [1, 8]]], [53, [[4, 4]]], [59, [[4, 4]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [104, 24, 16], 'galois_label': '16T31', 'galt': 31, 'grd': 48.49237211223896, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '16.0.1495873430980877352960000.2', 'local_algs': ['2.16.52.18', '3.8.6.1', '3.8.6.1', '5.4.0.1', '5.4.0.1', '5.8.4.1'], 'monogenic': 0, 'num_ram': 3, 'r2': 8, 'ramps': [2, 3, 5], 'rd': 32.4288037154, 'regulator': {'__RealLiteral__': 0, 'data': '84223.0358383', 'prec': 44}, 'res': {'gal': ['167281,0,476976,0,1664716,0,3693840,0,4759150,0,3198696,0,1564612,0,565344,0,279499,0,-8664,0,-15980,0,1200,0,634,0,24,0,-8,0,0,0,1'], 'sib': ['155086,-296976,282704,-189952,85976,-13224,-10240,8616,-2390,192,-68,184,-48,-32,28,-8,1']}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1, 1, 1], 'subfields': ['-2.0.1', '-3.0.1', '-6.0.1', '40.0.-16.0.1', '1.0.-4.0.1', '10.0.-8.0.1', '25.0.-60.0.44.0.-12.0.1', '94.-64.88.-88.58.-28.16.-4.1', '9.0.36.0.36.0.12.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{921161}{704320904} a^{14} + \\frac{9593}{14373896} a^{12} + \\frac{2233019}{704320904} a^{10} + \\frac{41217761}{704320904} a^{8} + \\frac{228305955}{704320904} a^{6} - \\frac{707621237}{704320904} a^{4} + \\frac{895248505}{704320904} a^{2} - \\frac{28945181}{14373896} \\)', '\\( \\frac{751}{14373896} a^{14} + \\frac{807}{7186948} a^{12} + \\frac{18435}{14373896} a^{10} - \\frac{3102}{1796737} a^{8} + \\frac{47677}{14373896} a^{6} + \\frac{6879}{7186948} a^{4} - \\frac{39935}{14373896} a^{2} - \\frac{1445149}{3593474} \\)', '\\( \\frac{4788405}{9860492656} a^{15} + \\frac{921161}{704320904} a^{14} + \\frac{3867}{28747792} a^{13} + \\frac{9593}{14373896} a^{12} + \\frac{26107259}{9860492656} a^{11} + \\frac{2233019}{704320904} a^{10} + \\frac{227936703}{9860492656} a^{9} + \\frac{41217761}{704320904} a^{8} + \\frac{1105397299}{9860492656} a^{7} + \\frac{228305955}{704320904} a^{6} - \\frac{3425884989}{9860492656} a^{5} - \\frac{707621237}{704320904} a^{4} + \\frac{8717741565}{9860492656} a^{3} + \\frac{895248505}{704320904} a^{2} - \\frac{359399055}{201234544} a - \\frac{14571285}{14373896} \\)', '\\( \\frac{1227011}{704320904} a^{14} + \\frac{514}{1796737} a^{12} + \\frac{1706923}{704320904} a^{10} + \\frac{7394161}{88040113} a^{8} + \\frac{320625769}{704320904} a^{6} - \\frac{125924263}{88040113} a^{4} + \\frac{1275037209}{704320904} a^{2} - \\frac{841237}{1796737} \\)', '\\( \\frac{4788405}{9860492656} a^{15} - \\frac{751}{14373896} a^{14} + \\frac{3867}{28747792} a^{13} - \\frac{807}{7186948} a^{12} + \\frac{26107259}{9860492656} a^{11} - \\frac{18435}{14373896} a^{10} + \\frac{227936703}{9860492656} a^{9} + \\frac{3102}{1796737} a^{8} + \\frac{1105397299}{9860492656} a^{7} - \\frac{47677}{14373896} a^{6} - \\frac{3425884989}{9860492656} a^{5} - \\frac{6879}{7186948} a^{4} + \\frac{8717741565}{9860492656} a^{3} + \\frac{39935}{14373896} a^{2} - \\frac{359399055}{201234544} a + \\frac{5038623}{3593474} \\)', '\\( \\frac{2924171}{2465123164} a^{15} - \\frac{751}{14373896} a^{14} + \\frac{20565}{12577159} a^{13} - \\frac{807}{7186948} a^{12} + \\frac{15045091}{4930246328} a^{11} - \\frac{18435}{14373896} a^{10} + \\frac{289280471}{4930246328} a^{9} + \\frac{3102}{1796737} a^{8} + \\frac{448055999}{1232561582} a^{7} - \\frac{47677}{14373896} a^{6} - \\frac{1404306663}{2465123164} a^{5} - \\frac{6879}{7186948} a^{4} + \\frac{1585002899}{4930246328} a^{3} + \\frac{39935}{14373896} a^{2} + \\frac{32443695}{100617272} a + \\frac{5038623}{3593474} \\)', '\\( \\frac{3955997}{1408641808} a^{15} - \\frac{1110885}{352160452} a^{14} + \\frac{525197}{201234544} a^{13} - \\frac{16933}{14373896} a^{12} + \\frac{14028383}{1408641808} a^{11} - \\frac{1436643}{176080226} a^{10} + \\frac{190535321}{1408641808} a^{9} - \\frac{97939081}{704320904} a^{8} + \\frac{1120804219}{1408641808} a^{7} - \\frac{276802035}{352160452} a^{6} - \\frac{2355249667}{1408641808} a^{5} + \\frac{1713667057}{704320904} a^{4} + \\frac{3694307593}{1408641808} a^{3} - \\frac{541593021}{176080226} a^{2} - \\frac{782928567}{201234544} a + \\frac{75984061}{14373896} \\)'], 'used_grh': True, 'zk': ['1', 'a', 'a^2', 'a^3', '1/2*a^4 - 1/2', '1/2*a^5 - 1/2*a', '1/2*a^6 - 1/2*a^2', '1/4*a^7 - 1/4*a^6 - 1/4*a^5 - 1/4*a^4 - 1/4*a^3 + 1/4*a^2 + 1/4*a + 1/4', '1/4*a^8 - 1/4', '1/4*a^9 - 1/4*a', '1/8*a^10 - 1/8*a^8 - 1/4*a^6 - 1/4*a^4 + 1/8*a^2 + 3/8', '1/8*a^11 - 1/8*a^9 - 1/4*a^6 - 1/4*a^4 - 1/8*a^3 + 1/4*a^2 + 1/8*a + 1/4', '1/8*a^12 - 1/8*a^8 - 1/8*a^4 + 1/8', '1/112*a^13 - 1/16*a^12 - 3/112*a^9 - 1/16*a^8 - 1/14*a^7 - 13/112*a^5 - 3/16*a^4 - 5/14*a^3 - 1/112*a + 5/16', '1/1408641808*a^14 + 137835/28747792*a^12 + 24479669/1408641808*a^10 - 93992585/1408641808*a^8 - 116847653/1408641808*a^6 - 221156535/1408641808*a^4 - 81305393/1408641808*a^2 - 5836635/28747792', '1/9860492656*a^15 + 137835/201234544*a^13 - 503761009/9860492656*a^11 - 974393715/9860492656*a^9 + 587473251/9860492656*a^7 - 1/4*a^6 + 483164369/9860492656*a^5 - 1/4*a^4 + 1151256189/9860492656*a^3 + 1/4*a^2 - 2243161/201234544*a + 1/4']}
Number field data - 16.0.1495873430980877352960000.2