Low Degree Fields Unramified Outside of {∞, 11, 19}

Discriminant class: −19

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

Discriminant class: −11

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

Discriminant class: 1

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

Discriminant class: 209

∞ 11 19 a_{1} a_{2} a_{3}  Over p = 11  Over p = 19 2 3 5 7 13 17 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_{i} 1_{k} 0 -209  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{k} 19 19  2  2  2
C_{2}  2 2  2  2 2 2