Low Degree Fields Unramified Outside of {∞, 2, 41}

Discriminant class: −82

∞ 2 41 a_{1} a_{2} a_{3}  Over p = 2  Over p = 41 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 37 43 47 53 59 61
1. 1_{k} 3_{i} 1_{+} 0 82  1^{2} 3_{i} −2 −2 1^{2} 1_{+} 41 41 2 2  2  2 2 2
C_{2} 4  2 2  2

Discriminant class: −41

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

Discriminant class: −2

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

Discriminant class: −1

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

Discriminant class: 2

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

Discriminant class: 41

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

Discriminant class: 82

∞ 2 41 a_{1} a_{2} a_{3} Over p = 2  Over p = 41 3 5 7 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 43 47 53 59 61
7. 0_{+} 3_{+} 1_{+} 0 -82  1^{2} 3_{+} 2 2 1^{2} 1_{+} 41 41  2 2  2
C_{2} 4  2 2 2  2 2