Low Degree Fields Unramified Outside of {∞, 31, 41}

Discriminant class: −1271

∞ 31 41 a_{1} a_{2} a_{3}  Over p = 31  Over p = 41 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 37 43 47 53 59 61
1. 1_{k} 1_{i} 1_{+} 0 1271  1^{2} 1_{i} 31∗ 31∗ 1^{2} 1_{+} 41 41  2  2
C_{2} 40  2  2 2 2  2

Discriminant class: −31

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

Discriminant class: 1

∞ 31 41 a_{1} a_{2} a_{3} Over p = 31 Over p = 41 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 37 43 47 53 59 61
4. 0_{+} 2_{+} 0_{+} 1 -10 -8 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3 3 3
C_{3}  3 3  3 3

Discriminant class: 41

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