Low Degree Fields Unramified Outside of {∞, 2, 47}

Discriminant class: −94

∞ 2 47 a_{1} a_{2} a_{3} Over p = 2  Over p = 47  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 41 43 53 59 61
1. 1_{k} 3_{+} 1_{i} 0 94  1^{2} 3_{+} 2 2 1^{2} 1_{i} 47∗ 47∗ 2  2
C_{2} 8  2 2 2  2 2 2

Discriminant class: −47

∞ 2 47 a_{1} a_{2} a_{3} Over p = 2  Over p = 47  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 41 43 53 59 61
2. 1_{k} 0_{+} 1_{i} 0 47  1^{2} 1_{i} 47∗ 47∗  2  2 2  2 2
C_{2} 5  2 2  2 2

Discriminant class: −2

∞ 2 47 a_{1} a_{2} a_{3}  Over p = 2  Over p = 47 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 41 43 53 59 61
3. 1_{k} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗  2 2  2  2
C_{2}  2 2 2  2  2
4. 1_{k} 3_{i} 2_{+} -1 16 40 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  3 2 2  2 3  2
S_{3}  2 2 2 3 3 2 3 2

Discriminant class: −1

∞ 2 47 a_{1} a_{2} a_{3}  Over p = 2  Over p = 47 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 41 43 53 59 61
5. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 2  2 2  2 2
C_{2}  2  2  2
6. 1_{k} 2_{i} 2_{+} -1 16 -54 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2 3 2 2 3 3 2 2
S_{3} 2 2 3 2 3

Discriminant class: 2

∞ 2 47 a_{1} a_{2} a_{3} Over p = 2  Over p = 47 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 41 43 53 59 61
7. 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: 47

∞ 2 47 a_{1} a_{2} a_{3}  Over p = 2  Over p = 47 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 41 43 53 59 61
8. 0_{+} 2_{i} 1_{k} 0 -47  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 47 47 2 2 2  2
C_{2}  2  2  2

Discriminant class: 94

∞ 2 47 a_{1} a_{2} a_{3}  Over p = 2  Over p = 47 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 41 43 53 59 61
9. 0_{+} 3_{i} 1_{k} 0 -94  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 47 47  2 2  2
C_{2}  2 2 2 2  2