data: - - class_group: [] class_number: 1 cm: false coeffs: - 1 - -1 - 9 - -10 - -6 - 11 - -1 - -3 - 1 conductor: 0 degree: 8 dirichlet_group: [] disc_abs: 8719893 disc_rad: 273 disc_sign: 1 frobs: - - 2 - - - 8 - 1 - - 3 - - 0 - - 5 - - - 8 - 1 - - 7 - - 0 - - 11 - - - 8 - 1 - - 13 - - 0 - - 17 - - - 2 - 4 - - 19 - - - 4 - 1 - - 1 - 4 - - 23 - - - 4 - 2 - - 29 - - - 2 - 4 - - 31 - - - 4 - 1 - - 1 - 4 - - 37 - - - 4 - 1 - - 2 - 2 - - 41 - - - 8 - 1 - - 43 - - - 2 - 2 - - 1 - 4 - - 47 - - - 8 - 1 - - 53 - - - 2 - 4 - - 59 - - - 8 - 1 gal_is_abelian: false gal_is_cyclic: false gal_is_solvable: true galois_disc_exponents: - 16 - 16 - 24 galois_label: 8T17 galt: 17 grd: 31.37380273734233 id: 12313394 index: 1 inessentialp: [] is_galois: false is_minimal_sibling: true iso_number: 1 label: 8.0.8719893.1 local_algs: - 3.8.4.1 - 7.2.1.2 - 7.2.1.2 - 7.4.0.1 - 13.4.3.3 - 13.4.0.1 monogenic: 0 num_ram: 3 r2: 4 ramps: - 3 - 7 - 13 rd: 7.37163620696 regulator: __RealLiteral__: 0 data: '3.28851213295' prec: 44 res: {} subfield_mults: - 1 - 1 subfields: - 1.-1.1 - 1.1.-1.-1.1 torsion_gen: \( \frac{1}{17} a^{7} + \frac{2}{17} a^{6} - \frac{8}{17} a^{5} - \frac{12}{17} a^{4} + \frac{36}{17} a^{3} + a^{2} - \frac{42}{17} a + \frac{10}{17} \) torsion_order: 6 units: - \( \frac{3}{17} a^{7} - \frac{11}{17} a^{6} - \frac{7}{17} a^{5} + \frac{49}{17} a^{4} - \frac{11}{17} a^{3} - 4 a^{2} + \frac{27}{17} a + \frac{13}{17} \) - \( \frac{4}{17} a^{7} - \frac{9}{17} a^{6} - \frac{15}{17} a^{5} + \frac{54}{17} a^{4} - \frac{9}{17} a^{3} - 4 a^{2} + \frac{53}{17} a - \frac{11}{17} \) - \( \frac{1}{17} a^{7} - \frac{15}{17} a^{6} + \frac{26}{17} a^{5} + \frac{39}{17} a^{4} - \frac{100}{17} a^{3} - a^{2} + \frac{94}{17} a - \frac{24}{17} \) used_grh: false zk: - '1' - a - a^2 - a^3 - a^4 - a^5 - a^6 - 1/17*a^7 + 2/17*a^6 - 8/17*a^5 + 5/17*a^4 + 2/17*a^3 - 8/17*a - 7/17 label_cols: - label labels: - 8.0.8719893.1 tables: - nf_fields timestamp: '2024-03-29T04:50:06.896138'