Low Degree Fields Unramified Outside of {∞, 17, 31}

Discriminant class: −527

∞ 17 31 a_{1} a_{2} a_{3}  Over p = 17  Over p = 31 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 527  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 31 31  2 2  2
C_{2} 18  2 2  2
2. 1_{k} 1_{−} 1_{k} 0 5 -1 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 31 31 3 3 2 2 3 2  3
S_{3}  3 2 2 3 2 3 3

Discriminant class: −31

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

Discriminant class: 1

∞ 17 31 a_{1} a_{2} a_{3} Over p = 17 Over p = 31 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
5. 0_{+} 0_{+} 2_{+} 1 -10 -8 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3
C_{3}  3 3 3  3 3

Discriminant class: 17

∞ 17 31 a_{1} a_{2} a_{3} Over p = 17 Over p = 31 2 3 5 7 11 13 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 37 41 43 47 53 59 61
6. 0_{+} 1_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2 2  2
C_{2}  2 2 2  2