Quintic Fields Unramified Outside of {∞, 2, 17}

Discriminant class: −17

∞  2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  3 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} 10_{k} 3_{−} -2 -4 24 1^{4} 10_{k} −1 2∗ 1^{3} 2_{+} ∗  3 4 5 5 5 4 5 32
S_{5} -4 -24 1^{2} 1_{−} 17∗ 17∗ 3 32 2 32 32 3 4 4

Discriminant class: 1

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

Discriminant class: 2

∞  2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17 3 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_{−} 11_{−} 2_{+} -1 -2 10 1^{4} 11_{−} 2 −2 1^{3} 2_{+} ∗  32 4 3 4 32 32 5 4
S_{5} -9 9 2 0_{+} ∗ ∗ 22 4 5 4 3 4 4 2

Discriminant class: 34

∞ 2 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  3 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
4. 2_{−} 9_{+} 3_{−} -2 6 -12 1^{4} 9_{+} 2 −1 1^{3} 2_{+} ∗  3 5 32 5 4 32 4 3
S_{5}  10 -12  1^{2} 1_{−} 17∗ 17∗ 4 5 32 2 22 32 4 3