Low Degree Fields Unramified Outside of {∞, 23, 61}

Discriminant class: −1403

∞ 23 61 a_{1} a_{2} a_{3}  Over p = 23  Over p = 61  2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d  s 29 31 37 41 43 47 53 59
1. 1_{k} 1_{k} 1_{−} 0 1403  1^{2} 1_{k} 23 23 1^{2} 1_{−} 61∗ 61∗ 2  2  2
C_{2} 14  2 2  2

Discriminant class: −23

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

Discriminant class: 1

∞ 23 61 a_{1} a_{2} a_{3} Over p = 23 Over p = 61 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
4. 0_{+} 0_{+} 2_{+} -1 -20 9  1^{3} 2_{+} 1  3  3 3  3 3 3
C_{3}  3 3  3 3  3

Discriminant class: 61

∞ 23 61 a_{1} a_{2} a_{3} Over p = 23  Over p = 61 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 41 43 47 53 59
5. 0_{+} 0_{+} 1_{+} 0 -61  2 0_{+} ∗ ∗ 1^{2} 1_{+} 61 61 2  2 2  2
C_{2}  2 2 2  2  2 2
6. 0_{+} 2_{+} 1_{+} 0 -46 -115 1^{3} 2_{+} ∗  1^{2} 1_{+} 61 61 2 3  2 2 3 2 3
S_{3}  2 2 2 3 2  2 2