Low Degree Fields Ramifying Above {13, 61}

Discriminant class: 1

∞ 13 61 a_{1} a_{2}  a_{3} Over p = 13 Over p = 61 2 3 5 7 11 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. 0_{+} 2_{+} 2_{+} -1 -264 1351 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3 3
C_{3} 3  3 3 3  3
2. 0_{+} 2_{+} 2_{+} -1 -264 -1028 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3
C_{3} 3  3 3 3 3 3 3  3

Discriminant class: 61

∞ 13 61 a_{1} a_{2} a_{3} Over p = 13  Over p = 61 2 3 5 7 11 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
3. 0_{+} 2_{+} 1_{+} -1 -17 -14 1^{3} 2_{+} 1  1^{2} 1_{+} 61 61 2 3 3 2 2 2 3 2
S_{3} 3 2 2 2 2 2 2

Discriminant class: 793

∞ 13 61 a_{1} a_{2} a_{3} Over p = 13 Over p = 61 2 3 5 7 11 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. 0_{+} 1_{+} 1_{+} 0 -793  1^{2} 1_{+} 13 13 1^{2} 1_{+} 61 61  2  2 2 2
C_{2} 4  2  2 2 2 2