Low Degree Fields Ramifying Above {2, 19, 29}

Discriminant class: −1102

∞ 2 19 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 19  Over p = 29 3 5 7 11 13 17 23 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_{i} 1_{+} 0 1102  1^{2} 3_{+} 2 2 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{+} 29 29 2 2  2
C_{2} 20  2  2

Discriminant class: −19

∞ 2 19 29 a_{1} a_{2} a_{3} Over p = 2  Over p = 19  Over p = 29 3 5 7 11 13 17 23 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_{+} 1_{i} 2_{+} -1 39 -43 1^{3} 2_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2 3  3 2 3  2
S_{3} 6  2 2  3 2 2 3 2
3. 1_{k} 2_{+} 1_{i} 2_{+} 0 58 -174 1^{3} 2_{+} ∗  1^{2} 1_{i} 19∗ 19∗ 1^{3} 2_{+} ∗  2  3 3 2 3  2
S_{3} 3  2 2 3  2 2  2

Discriminant class: −2

∞ 2 19 29 a_{1} a_{2}  a_{3}  Over p = 2  Over p = 19 Over p = 29 3 5 7 11 13 17 23 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. 1_{k} 3_{i} 2_{+} 2_{+} -1 -367 -2653 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  3 2 2  2  2 2
S_{3} 6  2 3 3 2 2 3 2 3
5. 1_{k} 3_{i} 2_{+} 2_{+} -1 184 3408 1^{2} 3_{i} −2 −2 1^{3} 2_{+} 1  1^{3} 2_{+} ∗  2 2 3 2  2 2
S_{3} 3  2  3 2 2 3 2 3

Discriminant class: 551

∞ 2 19 29 a_{1} a_{2} a_{3}  Over p = 2  Over p = 19  Over p = 29  3 5 7 11 13 17 23 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
6. 0_{+} 2_{i} 1_{i} 1_{−} 0 -551  1^{2} 2_{i} −1 −1 1^{2} 1_{i} 19∗ 19∗ 1^{2} 1_{−} 29∗ 29∗ 2  2  2 2 2 2
C_{2} 2  2  2

Discriminant class: 1102

∞ 2 19 29 a_{1}  a_{2} a_{3}  Over p = 2  Over p = 19  Over p = 29 3 5 7 11 13 17 23 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
7. 0_{+} 3_{i} 1_{k} 1_{+} 0 -1102  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 19 19 1^{2} 1_{+} 29 29  2 2 2  2 2 2
C_{2} 2  2  2  2  2