Low Degree Fields Ramifying Above {2, 13, 17}

Discriminant class: −442

∞ 2 13 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 17 3 5 7 11 19 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_{k} 1_{−} 1_{+} 0 442  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{+} 17 17 2 2 2  2  2
C_{2} 8  2  2 2  2

Discriminant class: −221

∞ 2 13 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 17 3 5 7 11 19 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_{+} 1_{+} 0 221  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 13 13 1^{2} 1_{+} 17 17  2 2  2 2
C_{2} 16  2  2

Discriminant class: −17

∞ 2 13 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 17 3 5 7 11 19 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. 1_{k} 2_{i} 2_{+} 1_{+} -1 -4 -40 1^{2} 2_{i} −1 −1 1^{3} 2_{+} 1  1^{2} 1_{+} 17 17 3 2 3  2 3 2 3
S_{3} 3  2 2 2 2 3 2 2 2

Discriminant class: 442

∞ 2 13 17 a_{1} a_{2} a_{3}  Over p = 2  Over p = 13  Over p = 17 3 5 7 11 19 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_{−} 1_{−} 1_{+} 0 -442  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{+} 17 17  2  2  2
C_{2} 8  2  2 2 2