Low Degree Fields Unramified Outside of {∞, 29, 47}

Discriminant class: −1363

∞ 29 47 a_{1} a_{2} a_{3}  Over p = 29  Over p = 47 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 31 37 41 43 53 59 61
1. 1_{k} 1_{−} 1_{k} 0 1363  1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 47 47 2 2 2  2 2
C_{2} 6  2  2  2
2. 1_{k} 1_{−} 1_{k} -1  -9 -10 1^{2} 1_{−} 29∗ 29∗ 1^{2} 1_{k} 47 47 2 2 2 3 3 2 2
S_{3}  2 3 2 3 3 3 3 2

Discriminant class: −47

∞ 29 47 a_{1} a_{2} a_{3} Over p = 29  Over p = 47  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 23 31 37 41 43 53 59 61
3. 1_{k} 0_{+} 1_{i} 0 47  2 0_{+} ∗ ∗ 1^{2} 1_{i} 47∗ 47∗  2  2 2  2
C_{2} 5  2 2  2 2
4. 1_{k} 2_{+} 1_{i} -1 -48 189 1^{3} 2_{+} ∗  1^{2} 1_{i} 47∗ 47∗ 3  2  2 2 3 2
S_{3} 2  2 2 3 2 2 3  3

Discriminant class: 29

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