Low Degree Fields Ramifying Above {2, 3}

Discriminant class: −6

∞ 2 3 a_{1} a_{2} a_{3} Over p = 2 Over p = 3 5 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_{−} 1_{k} 0 6  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 3 3  2 2 2 2
C_{2} 2  2 2 2 2  2
2. 1_{k} 3_{−} 3_{k} 0 3 -2 1^{2} 3_{−} 2∗ 2∗ 1^{3} 3_{k} 3  3 3 3 2 2 2 2
S_{3} 3 2 2 2 2 3 2

Discriminant class: −3

∞ 2 3 a_{1} a_{2} a_{3} Over p = 2  Over p = 3 5 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} 2_{+} 3_{i} 0 0 -2 1^{3} 2_{+} ∗  1^{3} 3_{i} 3∗  2 3 2 3 2 3 2 2
S_{3}  3 2  2 2 2 3
4. 1_{k} 2_{+} 5_{i} 0 0 -12 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2 3 2  2  2 2
S_{3}  3 3 2 3 2 2 2 3
5. 1_{k} 2_{+} 5_{i} 0 0 -6 1^{3} 2_{+} ∗  1^{3} 5_{i} 3∗  2  2 3 2 3 2 2
S_{3}  3  2 3 2 2 2 3

Discriminant class: −2

∞ 2 3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 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
6. 1_{k} 3_{i} 4_{+} 0 -3 -10 1^{2} 3_{i} −2 −2 1^{3} 4_{+} 1  2 2 3 2 3 3 2 2
S_{3} 3  2 2 3 3 2 2 3 2

Discriminant class: −1

∞ 2 3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 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
7. 1_{k} 2_{i} 4_{+} 0 -3 -4 1^{2} 2_{i} −1 −1 1^{3} 4_{+} ∗  3 2 2 3 3 2 2 3
S_{3} 2 3 2 2 2 3

Discriminant class: 3

∞ 2 3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3 5 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
8. 0_{+} 2_{i} 1_{k} 0 -3  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 3 3 2 2  2 2  2
C_{2}  2  2 2  2

Discriminant class: 6

∞ 2 3 a_{1} a_{2} a_{3}  Over p = 2  Over p = 3  5 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
9. 0_{+} 3_{k} 1_{i} 0 -6  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 3∗ 3∗  2 2 2 2
C_{2}  2 2 2  2 2
10. 0_{+} 3_{k} 5_{i} 0 -9 -6 1^{2} 3_{k} −2∗ −2∗ 1^{3} 5_{i} 3∗  3 2 2 2 2 3 3 3
S_{3}  2 2 2  3 3 2 2