Low Degree Fields Unramified Outside of {∞, 17, 23}

Discriminant class: −391

∞ 17 23 a_{1} a_{2} a_{3}  Over p = 17  Over p = 23 2 3 5 7 11 13 19 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 391  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23  2  2 2
C_{2} 14  2  2 2  2

Discriminant class: −23

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

Discriminant class: 17

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