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nf_fields • Show schema
{'class_group': [], 'class_number': 1, 'cm': False, 'coeffs': [288, 0, -432, 0, 225, 0, -84, 0, 42, 0, -12, 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, [[3, 2], [2, 2], [1, 2]]], [11, [[4, 3]]], [13, [[12, 1]]], [17, [[6, 2]]], [19, [[4, 3]]], [23, [[6, 1], [2, 3]]], [29, [[12, 1]]], [31, [[2, 6]]], [37, [[4, 3]]], [41, [[2, 4], [1, 4]]], [43, [[4, 3]]], [47, [[3, 2], [2, 2], [1, 2]]], [53, [[12, 1]]], [59, [[4, 3]]]], 'gal_is_abelian': False, 'gal_is_cyclic': False, 'gal_is_solvable': True, 'galois_disc_exponents': [486, 200], 'galois_label': '12T79', 'galt': 79, 'grd': 47.713870191292706, 'index': 1, 'inessentialp': [], 'is_galois': False, 'is_minimal_sibling': True, 'iso_number': 2, 'label': '12.8.657366253849018368.2', 'local_algs': ['2.1.4.11a1.10', '2.1.8.26c1.12', '3.2.6.14a1.2'], 'monogenic': 0, 'narrow_class_group': [2], 'narrow_class_number': 2, 'num_ram': 2, 'r2': 2, 'ramps': [2, 3], 'rd': 30.5363611839, 'regulator': {'__RealLiteral__': 0, 'data': '153152.048963', 'prec': 44}, 'res': {}, 'subfield_mults': [1, 1, 1], 'subfields': ['-2.0.1', '18.0.-12.0.1', '-4.12.9.-4.-6.0.1'], 'torsion_gen': '\\( -1 \\)', 'torsion_order': 2, 'units': ['\\( \\frac{1}{372} a^{10} - \\frac{7}{186} a^{8} + \\frac{35}{186} a^{6} - \\frac{27}{62} a^{4} + \\frac{59}{124} a^{2} - \\frac{19}{31} \\)', '\\( \\frac{7}{124} a^{10} - \\frac{67}{124} a^{8} + \\frac{385}{372} a^{6} - \\frac{235}{124} a^{4} + \\frac{209}{31} a^{2} - \\frac{213}{31} \\)', '\\( \\frac{1}{186} a^{11} + \\frac{3}{62} a^{10} - \\frac{7}{93} a^{9} - \\frac{95}{186} a^{8} + \\frac{109}{372} a^{7} + \\frac{485}{372} a^{6} - \\frac{23}{62} a^{5} - \\frac{145}{62} a^{4} + \\frac{149}{124} a^{3} + \\frac{969}{124} a^{2} - \\frac{169}{62} a - \\frac{311}{31} \\)', '\\( \\frac{7}{744} a^{11} + \\frac{35}{372} a^{10} - \\frac{49}{372} a^{9} - \\frac{335}{372} a^{8} + \\frac{61}{124} a^{7} + \\frac{163}{93} a^{6} - \\frac{65}{124} a^{5} - \\frac{433}{124} a^{4} + \\frac{661}{248} a^{3} + \\frac{1507}{124} a^{2} - \\frac{257}{62} a - \\frac{355}{31} \\)', '\\( \\frac{35}{248} a^{11} + \\frac{8}{31} a^{10} - \\frac{259}{186} a^{9} - \\frac{81}{31} a^{8} + \\frac{551}{186} a^{7} + \\frac{2225}{372} a^{6} - \\frac{174}{31} a^{5} - \\frac{335}{31} a^{4} + \\frac{5017}{248} a^{3} + \\frac{4703}{124} a^{2} - \\frac{1189}{62} a - \\frac{1235}{31} \\)', '\\( \\frac{1}{186} a^{11} - \\frac{43}{372} a^{10} - \\frac{7}{93} a^{9} + \\frac{149}{124} a^{8} + \\frac{109}{372} a^{7} - \\frac{272}{93} a^{6} - \\frac{23}{62} a^{5} + \\frac{617}{124} a^{4} + \\frac{149}{124} a^{3} - \\frac{2227}{124} a^{2} - \\frac{169}{62} a + \\frac{631}{31} \\)', '\\( \\frac{1}{12} a^{10} - \\frac{5}{6} a^{8} + \\frac{11}{6} a^{6} - \\frac{7}{2} a^{4} + \\frac{55}{4} a^{2} - 15 \\)', '\\( \\frac{1}{186} a^{11} + \\frac{43}{372} a^{10} - \\frac{7}{93} a^{9} - \\frac{149}{124} a^{8} + \\frac{109}{372} a^{7} + \\frac{272}{93} a^{6} - \\frac{23}{62} a^{5} - \\frac{617}{124} a^{4} + \\frac{149}{124} a^{3} + \\frac{2227}{124} a^{2} - \\frac{169}{62} a - \\frac{631}{31} \\)', '\\( \\frac{55}{744} a^{11} + \\frac{1}{372} a^{10} - \\frac{73}{93} a^{9} - \\frac{7}{186} a^{8} + \\frac{249}{124} a^{7} + \\frac{35}{186} a^{6} - \\frac{100}{31} a^{5} - \\frac{27}{62} a^{4} + \\frac{2749}{248} a^{3} + \\frac{59}{124} a^{2} - \\frac{414}{31} a + \\frac{43}{31} \\)'], 'used_grh': False, 'zk': ['1', 'a', 'a^2', 'a^3', 'a^4', '1/2*a^5 - 1/2*a', '1/6*a^6 - 1/2*a^2', '1/12*a^7 - 1/12*a^6 - 1/4*a^3 + 1/4*a^2', '1/12*a^8 - 1/12*a^6 - 1/4*a^4 + 1/4*a^2', '1/12*a^9 - 1/12*a^6 - 1/4*a^5 + 1/4*a^2', '1/372*a^10 - 7/186*a^8 + 2/93*a^6 - 27/62*a^4 - 3/124*a^2 + 12/31', '1/744*a^11 - 7/372*a^9 + 1/93*a^7 - 27/124*a^5 - 3/248*a^3 - 19/62*a']}
Number field data - 12.8.657366253849018368.2