Low Degree Fields Unramified Outside of {∞, 17, 19}

Discriminant class: −323

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

Discriminant class: −19

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

Discriminant class: 1

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

Discriminant class: 17

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