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nf_fields • Show schema
{'class_group': [4], 'class_number': 4, 'cm': False, 'coeffs': [25, 0, -75, 0, 260, 0, -450, 0, 196, 0, 108, 0, 49, 0, 7, 0, 1], 'conductor': 0, 'degree': 16, 'dirichlet_group': [], 'disc_abs': 17944209936000000000000, 'disc_rad': 1830, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [0]], [7, [[8, 2]]], [11, [[4, 2], [2, 4]]], [13, [[4, 4]]], [17, [[8, 2]]], [19, [[2, 4], [1, 8]]], [23, [[8, 2]]], [29, [[2, 8]]], [31, [[2, 8]]], [37, [[8, 2]]], [41, [[4, 4]]], [43, [[8, 2]]], [47, [[4, 4]]], [53, [[8, 2]]], [59, [[2, 4], [1, 8]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [128, 64, 96, 64], 'galois_label': '16T227', 'galt': 227, 'grd': 90.46551164752914, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 1, 'label': '16.0.17944209936000000000000.1', 'local_algs': ['2.8.2.16a1.1', '3.4.1.0a1.1', '3.4.1.0a1.1', '3.4.2.4a1.2', '5.1.4.3a1.1', '5.1.4.3a1.1', '5.2.4.6a1.2', '61.2.1.0a1.1', '61.2.1.0a1.1', '61.2.1.0a1.1', '61.2.1.0a1.1', '61.2.2.2a1.2', '61.2.2.2a1.2'], 'maximal_cm_subfield': [625, 0, 375, 0, 105, 0, 15, 0, 1], 'monogenic': 0, 'narrow_class_group': [4], 'narrow_class_number': 4, 'num_ram': 4, 'r2': 8, 'ramps': [2, 3, 5, 61], 'rd': 24.596327743998025, 'regulator': {'__RealLiteral__': 0, 'data': '10557.253437747004', 'prec': 60}, 'subfield_mults': [1, 1, 1, 1, 1, 1, 1], 'subfields': ['-1.-1.1', '5.0.-5.0.1', '5.-5.6.-2.1', '305.0.35.0.1', '45.0.60.0.34.0.9.0.1', '1.2.2.-1.-1.1.2.-2.1', '625.0.375.0.105.0.15.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( -\\frac{14607633}{1360898275} a^{14} - \\frac{98539321}{1360898275} a^{12} - \\frac{679524057}{1360898275} a^{10} - \\frac{119741504}{123718025} a^{8} - \\frac{1943040228}{1360898275} a^{6} + \\frac{1743480406}{272179655} a^{4} - \\frac{619108153}{272179655} a^{2} + \\frac{29350966}{54435931} \\)', '\\( \\frac{2887}{136705} a^{14} + \\frac{21266}{136705} a^{12} + \\frac{148927}{136705} a^{10} + \\frac{362884}{136705} a^{8} + \\frac{674743}{136705} a^{6} - \\frac{1127703}{136705} a^{4} + \\frac{37832}{27341} a^{2} + \\frac{15540}{27341} \\)', '\\( \\frac{691851}{54435931} a^{14} + \\frac{6869031}{54435931} a^{12} + \\frac{49687716}{54435931} a^{10} + \\frac{16932716}{4948721} a^{8} + \\frac{440256882}{54435931} a^{6} + \\frac{311668175}{54435931} a^{4} - \\frac{287967138}{54435931} a^{2} + \\frac{34800022}{54435931} \\)', '\\( -\\frac{496654}{123718025} a^{14} - \\frac{3768243}{123718025} a^{12} - \\frac{26209656}{123718025} a^{10} - \\frac{67881052}{123718025} a^{8} - \\frac{129468674}{123718025} a^{6} + \\frac{26037029}{24743605} a^{4} - \\frac{13807014}{24743605} a^{2} + a - \\frac{2823447}{4948721} \\)', '\\( -\\frac{16480001}{1360898275} a^{15} - \\frac{2887}{136705} a^{14} - \\frac{105290507}{1360898275} a^{13} - \\frac{21266}{136705} a^{12} - \\frac{737567719}{1360898275} a^{11} - \\frac{148927}{136705} a^{10} - \\frac{117179993}{123718025} a^{9} - \\frac{362884}{136705} a^{8} - \\frac{2171760076}{1360898275} a^{7} - \\frac{674743}{136705} a^{6} + \\frac{1870148788}{272179655} a^{5} + \\frac{1127703}{136705} a^{4} - \\frac{1829285811}{272179655} a^{3} - \\frac{37832}{27341} a^{2} + \\frac{192174839}{54435931} a - \\frac{15540}{27341} \\)', '\\( -\\frac{77155424}{1360898275} a^{15} - \\frac{38732228}{1360898275} a^{14} - \\frac{551027418}{1360898275} a^{13} - \\frac{298995731}{1360898275} a^{12} - \\frac{3861795981}{1360898275} a^{11} - \\frac{2098354327}{1360898275} a^{10} - \\frac{809724832}{123718025} a^{9} - \\frac{507483794}{123718025} a^{8} - \\frac{16576242849}{1360898275} a^{7} - \\frac{10808567283}{1360898275} a^{6} + \\frac{6363115782}{272179655} a^{5} + \\frac{2336410887}{272179655} a^{4} - \\frac{3309512124}{272179655} a^{3} + \\frac{500936652}{272179655} a^{2} + \\frac{214230219}{54435931} a - \\frac{30189680}{54435931} \\)', '\\( \\frac{38732228}{1360898275} a^{15} + \\frac{2887}{136705} a^{14} + \\frac{298995731}{1360898275} a^{13} + \\frac{21266}{136705} a^{12} + \\frac{2098354327}{1360898275} a^{11} + \\frac{148927}{136705} a^{10} + \\frac{507483794}{123718025} a^{9} + \\frac{362884}{136705} a^{8} + \\frac{10808567283}{1360898275} a^{7} + \\frac{674743}{136705} a^{6} - \\frac{2336410887}{272179655} a^{5} - \\frac{1127703}{136705} a^{4} - \\frac{500936652}{272179655} a^{3} + \\frac{37832}{27341} a^{2} + \\frac{30189680}{54435931} a - \\frac{11801}{27341} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', 'a^5', 'a^6', 'a^7', 'a^8', 'a^9', 'a^10', 'a^11', '1/5*a^12 + 2/5*a^10 - 1/5*a^8 - 2/5*a^6 + 1/5*a^4', '1/5*a^13 + 2/5*a^11 - 1/5*a^9 - 2/5*a^7 + 1/5*a^5', '1/1360898275*a^14 + 131672142/1360898275*a^12 + 354612689/1360898275*a^10 + 30386508/123718025*a^8 + 165495856/1360898275*a^6 + 26970484/272179655*a^4 + 101191166/272179655*a^2 - 10279391/54435931', '1/1360898275*a^15 + 131672142/1360898275*a^13 + 354612689/1360898275*a^11 + 30386508/123718025*a^9 + 165495856/1360898275*a^7 + 26970484/272179655*a^5 + 101191166/272179655*a^3 - 10279391/54435931*a']}
Number field data - 16.0.17944209936000000000000.1