Low Degree Fields Ramifying Above {3, 5}

Discriminant class: −15

∞ 3 5 a_{1} a_{2} a_{3} Over p = 3 Over p = 5 2 7 11 13 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 1_{k} 1_{k} 1_{−} 0 15  1^{2} 1_{k} 3 3 1^{2} 1_{−} 5∗ 5∗  2 2 2  2
C_{2} 2  2 2 2  2
2. 1_{k} 3_{k} 1_{−} 0 3 -1 1^{3} 3_{k} 3  1^{2} 1_{−} 5∗ 5∗ 3 2 2 2 3 3 3 2
S_{3} 3 2 2 2 3 2 3

Discriminant class: −3

∞ 3 5 a_{1} a_{2} a_{3} Over p = 3 Over p = 5 2 7 11 13 17 19 23 29
G h  f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
3. 1_{k} 3_{i} 2_{+} 0 0 -5 1^{3} 3_{i} 3∗ 1^{3} 2_{+} ∗ 2 3 2 2 3 2 2
S_{3}  3 3 2 3 2 2 2 3
4. 1_{k} 5_{i} 2_{+} 0 0 -45 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 3 2 3 2  2 2
S_{3}  3  2  2 2 2 3
5. 1_{k} 5_{i} 2_{+} 0 0 -15 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2  2 3 2 3 2 2
S_{3} 2  3 2 3 2 2 2 3