Low Degree Fields Ramifying Above {2, 61}

Discriminant class: −122

∞ 2 61 a_{1} a_{2} a_{3}  Over p = 2  Over p = 61  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 47 53 59
1. 1_{k} 3_{k} 1_{−} 0 122  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 61∗ 61∗  2  2 2 2
C_{2} 10  2 2  2

Discriminant class: −61

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

Discriminant class: −1

∞ 2 61 a_{1} a_{2} a_{3}  Over p = 2  Over p = 61 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 47 53 59
4. 1_{k} 2_{i} 2_{+} -1 -20 -52 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  2 3 2 2  2 2
S_{3} 3  3 2 3 3 2 2 3 2

Discriminant class: 122

∞ 2 61 a_{1} a_{2} a_{3}  Over p = 2  Over p = 61  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 47 53 59
5. 0_{+} 3_{−} 1_{−} 0 -122  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 61∗ 61∗ 2 2 2  2 2 2 2
C_{2} 2  2