Low Degree Fields Ramifying Above {7, 13, 19}

Discriminant class: −91

∞ 7 13 19 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 19 2 3 5 11 17 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{k} 1_{−} 2_{+} -1 13 26 1^{2} 1_{k} 7 7 1^{2} 1_{−} 13∗ 13∗ 1^{3} 2_{+} 1  2 2 3 2 2 3 3 3
S_{3} 3 2 3 3 3 2 2

Discriminant class: 1

∞ 7 13 19 a_{1} a_{2} a_{3} Over p = 7 Over p = 13 Over p = 19 2 3 5 11 17 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
2. 0_{+} 2_{+} 2_{+} 2_{+} -1 -576  64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3  3
C_{3} 9  3 3  3 3 3 3
3. 0_{+} 2_{+} 2_{+} 2_{+} -1 -576 -1665 1^{3} 2_{+} 1  1^{3} 2_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3
C_{3} 9  3  3  3  3
4. 0_{+} 2_{+} 2_{+} 2_{+} -1 -576 5251 1^{3} 2_{+} 1  1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3
C_{3} 9  3  3 3  3 3
5. 0_{+} 2_{+} 2_{+} 2_{+} -1 -576 -5123 1^{3} 2_{+} 1  1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3 3 3
C_{3} 9  3  3 3 3

Discriminant class: 1729

∞ 7 13 19 a_{1}  a_{2} a_{3} Over p = 7  Over p = 13  Over p = 19  2 3 5 11 17 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
6. 0_{+} 1_{k} 1_{+} 1_{i} 0 -1729  1^{2} 1_{k} 7 7 1^{2} 1_{+} 13 13 1^{2} 1_{i} 19∗ 19∗  2 2  2 2
C_{2} 2  2  2 2 2