Quintic Fields Unramified Outside of {∞, 3, 17}

Discriminant class: −3

∞ 3 17 a_{1} a_{2} a_{3}  Over p = 3  Over p = 17 2 5 7 11 13 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} 5_{i} 4_{+} 2 -12 2 1^{3} 5_{i} 3∗  1^{5} 4_{+} ∗  4 32 22 32 5 3 4 4
S_{5}  -20 63  5 5 2 22 4 4 32 5

Discriminant class: 1

∞ 3 17 a_{1} a_{2} a_{3}  Over p = 3  Over p = 17 2 5 7 11 13 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_{−} 6_{−} 2_{+} -2 4 -5 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  5 3 22 5 5 22 3 3
A_{5}  4 -5  1^{2} 1_{i} 3∗ 3∗ 2 0_{+} ∗ ∗ 5 5 3 22 5 5 3 5

Discriminant class: 17

∞ 3 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 17 2 5 7 11 13 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
3. 2_{−} 2_{−} 3_{+} -1 0 1 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{+} 17 17 5 4 4 4 5 22 4 4
F_{5}  3 1  4 4 4 22 22 5 5 4