Low Degree Fields Unramified Outside of {∞, 7, 47}

Discriminant class: −47

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7  Over p = 47  2 3 5 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} 0_{+} 1_{i} 0 47  1^{2} 1_{i} 47∗ 47∗  2 2 2  2 2
C_{2} 5  2 2  2 2
2. 1_{k} 2_{+} 1_{i} -1 -2 -27 1^{3} 2_{+} 1  1^{2} 1_{i} 47∗ 47∗ 3  2 2 2 3 2 2
S_{3} 3  2 2 3 2 2 3 3 3

Discriminant class: −7

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7 Over p = 47 2 3 5 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} 1_{i} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗  2 2  2 2 2
C_{2}  2  2  2 2
4. 1_{k} 1_{i} 2_{+} -1 16 -7 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 2 2 3 2 2 2 3
S_{3} 2  2 3 2 3 3 2 2

Discriminant class: 1

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7  Over p = 47 2 3 5 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. 0_{+} 2_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3  3 3 3
C_{3}  3 3  3 3 3

Discriminant class: 329

∞ 7 47 a_{1} a_{2} a_{3} Over p = 7 Over p = 47 2 3 5 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
6. 0_{+} 1_{i} 1_{k} 0 -329  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{k} 47 47  2  2  2  2
C_{2}  2  2  2 2