Low Degree Fields Unramified Outside of {∞, 11, 37}

Discriminant class: −407

∞ 11 37 a_{1} a_{2} a_{3}  Over p = 11  Over p = 37 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
1. 1_{k} 1_{i} 1_{+} 0 407  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 37 37  2 2  2
C_{2} 16  2 2  2

Discriminant class: −11

∞ 11 37 a_{1} a_{2} a_{3}  Over p = 11  Over p = 37 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
2. 1_{k} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗  2  2 2 2 2
C_{2}  2  2 2  2
3. 1_{k} 1_{i} 2_{+} -1 -12 100 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} 1  2 3  2 2 2 2 3
S_{3} 3  2  2 2 3 3 3 2

Discriminant class: 1

∞ 11 37 a_{1} a_{2} a_{3} Over p = 11 Over p = 37 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
4. 0_{+} 0_{+} 2_{+} 1 -12 11  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3}  3  3 3 3

Discriminant class: 37

∞ 11 37 a_{1} a_{2} a_{3} Over p = 11  Over p = 37 2 3 5 7 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
5. 0_{+} 0_{+} 1_{+} 0 -37  1^{2} 1_{+} 37 37 2  2  2 2 2 2
C_{2}  2 2  2  2 2