Quintic Fields Unramified Outside of {∞, 2, 7}

Discriminant class: −1

∞  2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 5 11 13 17 19 23 29
G  h  a_{4} a_{5}  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 10_{i} 4_{+} -1 -8 -4 1^{4} 10_{i} −1 2∗ 1^{5} 4_{+} ∗  32 3 32 5 5 4 4 5
S_{5} 6 2 4 3 5 4 32 3 4 22

Discriminant class: 14

∞  2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 5 11 13 17 19 23 29
G  h  a_{4} a_{5}  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
2. 2_{−} 11_{k} 3_{k} 0 -2 -4 1^{4} 11_{k} −2 −2∗ 1^{3} 2_{+} 1  32 5 5 3 4 4 32 4
S_{5}  -5 -4  1^{2} 1_{k} 7 7 5 4 4 5 3 4 2 3