-
nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [72, 0, -864, 0, 360, 0, -120, 0, -39, 0, 6, 0, 1], 'conductor': 0, 'degree': 12, 'dirichlet_group': [], 'disc_abs': 657366253849018368, 'disc_rad': 6, 'disc_sign': 1, 'frobs': [[2, [0]], [3, [0]], [5, [[12, 1]]], [7, [[6, 1], [2, 3]]], [11, [[8, 1], [2, 2]]], [13, [[12, 1]]], [17, [[6, 2]]], [19, [[8, 1], [2, 2]]], [23, [[4, 1], [3, 2], [2, 1]]], [29, [[12, 1]]], [31, [[4, 1], [2, 1], [1, 6]]], [37, [[4, 1], [2, 4]]], [41, [[2, 4], [1, 4]]], [43, [[8, 1], [2, 2]]], [47, [[6, 1], [4, 1], [1, 2]]], [53, [[12, 1]]], [59, [[8, 1], [2, 2]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [9864, 3200], 'galois_label': '12T237', 'galt': 237, 'grd': 89.42379121066101, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': False, 'iso_number': 9, 'label': '12.4.657366253849018368.9', 'local_algs': ['2.1.4.8b1.6', '2.1.8.29a1.20', '3.2.6.14a1.2'], 'minimal_sibling': [-23, -294, 879, -1014, 579, -36, -238, 204, -69, -6, 15, -6, 1], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 4, 'ramps': [2, 3], 'rd': 30.5363611839, 'regulator': {'__RealLiteral__': 0, 'data': '58908.8441685', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1], 'subfields': ['-2.0.1', '-4.12.9.-4.-6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{2}{591} a^{10} + \\frac{11}{591} a^{8} - \\frac{167}{1182} a^{6} - \\frac{165}{394} a^{4} + \\frac{232}{197} a^{2} - \\frac{495}{197} \\)', '\\( \\frac{5}{115836} a^{10} + \\frac{457}{57918} a^{8} + \\frac{3091}{115836} a^{6} - \\frac{4905}{19306} a^{4} + \\frac{933}{9653} a^{2} - \\frac{7229}{9653} \\)', '\\( \\frac{121}{28959} a^{10} + \\frac{937}{57918} a^{8} - \\frac{13945}{57918} a^{6} - \\frac{2972}{9653} a^{4} + \\frac{34327}{9653} a^{2} - \\frac{24333}{9653} \\)', '\\( \\frac{359}{57918} a^{11} - \\frac{3}{9653} a^{10} + \\frac{2467}{57918} a^{9} + \\frac{295}{57918} a^{8} - \\frac{11393}{57918} a^{7} + \\frac{1607}{28959} a^{6} - \\frac{16237}{19306} a^{5} - \\frac{4675}{19306} a^{4} + \\frac{12351}{9653} a^{3} - \\frac{14440}{9653} a^{2} - \\frac{52651}{9653} a + \\frac{15919}{9653} \\)', '\\( \\frac{359}{57918} a^{11} + \\frac{3}{9653} a^{10} + \\frac{2467}{57918} a^{9} - \\frac{295}{57918} a^{8} - \\frac{11393}{57918} a^{7} - \\frac{1607}{28959} a^{6} - \\frac{16237}{19306} a^{5} + \\frac{4675}{19306} a^{4} + \\frac{12351}{9653} a^{3} + \\frac{14440}{9653} a^{2} - \\frac{52651}{9653} a - \\frac{15919}{9653} \\)', '\\( \\frac{2365}{38612} a^{11} + \\frac{715}{38612} a^{10} + \\frac{14485}{38612} a^{9} + \\frac{12881}{115836} a^{8} - \\frac{135377}{57918} a^{7} - \\frac{14113}{19306} a^{6} - \\frac{73278}{9653} a^{5} - \\frac{22699}{9653} a^{4} + \\frac{204179}{9653} a^{3} + \\frac{62402}{9653} a^{2} - \\frac{490494}{9653} a - \\frac{144665}{9653} \\)', '\\( \\frac{3865}{115836} a^{11} - \\frac{3049}{115836} a^{10} + \\frac{23917}{115836} a^{9} - \\frac{4769}{38612} a^{8} - \\frac{78835}{57918} a^{7} + \\frac{13485}{9653} a^{6} - \\frac{48612}{9653} a^{5} + \\frac{28968}{9653} a^{4} + \\frac{132376}{9653} a^{3} - \\frac{184754}{9653} a^{2} - \\frac{59606}{9653} a + \\frac{32953}{9653} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a^3', '1/6*a^6 - 1/2*a^4', '1/6*a^7 - 1/2*a^3', '1/42*a^8 - 1/14*a^6 - 1/7*a^4 - 2/7', '1/84*a^9 - 1/84*a^8 - 1/28*a^7 + 1/28*a^6 - 1/14*a^5 + 1/14*a^4 - 1/7*a + 1/7', '1/115836*a^10 + 643/57918*a^8 + 1677/38612*a^6 + 1777/19306*a^4 - 1744/9653*a^2 - 2549/9653', '1/115836*a^11 - 31/38612*a^9 - 1/84*a^8 + 764/9653*a^7 + 1/28*a^6 + 1578/9653*a^5 + 1/14*a^4 - 1744/9653*a^3 - 1170/9653*a + 1/7']}
Number field data - 12.4.657366253849018368.9