Low Degree Fields Ramifying Above {2, 5}

Discriminant class: −10

∞ 2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5  3 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} 3_{k} 1_{−} 0 10  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{−} 5∗ 5∗ 2  2  2
C_{2} 2  2  2  2

Discriminant class: −5

∞ 2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 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
2. 1_{k} 2_{i} 1_{+} 0 5  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 5 5  2 2 2 2
C_{2} 2  2 2  2 2

Discriminant class: −2

∞ 2 5 a_{1} a_{2} a_{3}  Over p = 2  Over p = 5 3 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_{+} -1 2 2 1^{2} 3_{i} −2 −2 1^{3} 2_{+} ∗  3 2 3 2 3 3 2 2
S_{3} 2 2 3 2 2 2

Discriminant class: 10

∞ 2 5 a_{1} a_{2} a_{3} Over p = 2 Over p = 5 3 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
4. 0_{+} 3_{−} 1_{−} 0 -10  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{−} 5∗ 5∗  2 2  2 2 2 2
C_{2} 2  2  2 2