Low Degree Fields Unramified Outside of {∞, 11, 23}

Discriminant class: −23

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

Discriminant class: −11

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

Discriminant class: 253

∞ 11 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 23  2 3 5 7 13 17 19 29
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
4. 0_{+} 1_{k} 1_{i} 0 -253  1^{2} 1_{k} 11 11 1^{2} 1_{i} 23∗ 23∗ 2  2  2  2
C_{2}  2 2  2