Low Degree Fields Ramifying Above {61, 67}

Discriminant class: −4087

∞ 61 67 a_{1} a_{2} a_{3}  Over p = 61  Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
1. 1_{k} 1_{−} 1_{k} 0 4087  1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{k} 67 67  2 2  2 2
C_{2} 30  2 2  2 2
2. 1_{k} 1_{−} 1_{k} -1  2 24 1^{2} 1_{−} 61∗ 61∗ 1^{2} 1_{k} 67 67  2 2 3 3 2 2 3
S_{3}  2 2 3 2 2 3 3 3

Discriminant class: 1

∞ 61 67 a_{1} a_{2} a_{3} Over p = 61 Over p = 67 2 3 5 7 11 13 17 19
G h  f^{e} c_{w} d s f^{e} c_{w} d s 23 29 31 37 41 43 47 53
3. 0_{+} 2_{+} 2_{+} -1 -1362 -17559 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 3 3 3
C_{3} 3  3 3 3 3 3 3 3
4. 0_{+} 2_{+} 2_{+} 1 -1362 -19224 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3
C_{3} 3  3  3 3 3