Low Degree Fields Ramifying Above {2, 13, 19}

Discriminant class: −494

∞ 2 13 19 a_{1} a_{2} a_{3} Over p = 2  Over p = 13  Over p = 19  3 5 7 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} 3_{+} 1_{+} 1_{i} 0 494  1^{2} 3_{+} 2 2 1^{2} 1_{+} 13 13 1^{2} 1_{i} 19∗ 19∗  2
C_{2} 28  2  2 2  2 2 2

Discriminant class: −13

∞ 2 13 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 19 3 5 7 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. 1_{k} 2_{i} 1_{+} 2_{+} -1 32 -50 1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 13 13 1^{3} 2_{+} 1  2 2  3 3 2 3 3
S_{3} 3  2 2 2 3 3  3 3

Discriminant class: 247

∞ 2 13 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 19  3 5 7 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
3. 0_{+} 2_{i} 1_{−} 1_{i} 0 -247  1^{2} 2_{i} −1 −1 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{i} 19∗ 19∗  2  2 2 2
C_{2} 2  2  2 2  2

Discriminant class: 494

∞ 2 13 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 19 3 5 7 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
4. 0_{+} 3_{i} 1_{+} 1_{k} 0 -494  1^{2} 3_{i} −2 −2 1^{2} 1_{+} 13 13 1^{2} 1_{k} 19 19 2  2  2  2
C_{2} 2  2  2