Low Degree Fields Ramifying Above {2, 17, 19}

Discriminant class: −646

∞ 2 17 19 a_{1} a_{2} a_{3} Over p = 2 Over p = 17 Over p = 19 3 5 7 11 13 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_{−} 1_{+} 1_{k} 0 646  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 19 19 2  2  2 2
C_{2} 16  2  2

Discriminant class: −323

∞ 2 17 19 a_{1} a_{2} a_{3} Over p = 2  Over p = 17  Over p = 19  3 5 7 11 13 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_{+} 1_{+} 1_{i} 0 -10 -14 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗ 3 2 2 2 2 2 3 3
S_{3}  3 3 2 2 2 2

Discriminant class: −34

∞ 2 17 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 19 3 5 7 11 13 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} 3_{i} 1_{+} 2_{+} -1 -6 -126 1^{2} 3_{i} −2 −2 1^{2} 1_{+} 17 17 1^{3} 2_{+} 1  2 3  2 2 3 3 3
S_{3} 9  3 2 3 2 2 3

Discriminant class: 323

∞ 2 17 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 19 3 5 7 11 13 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_{+} 2_{i} 1_{+} 1_{k} 0 -323  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 19 19 2 2  2  2
C_{2} 4  2 2 2  2

Discriminant class: 646

∞ 2 17 19 a_{1} a_{2} a_{3}  Over p = 2  Over p = 17  Over p = 19  3 5 7 11 13 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
5. 0_{+} 3_{k} 1_{+} 1_{i} 0 -646  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{+} 17 17 1^{2} 1_{i} 19∗ 19∗  2  2 2
C_{2} 8  2  2  2  2