Low Degree Fields Unramified Outside of {∞, 2, 11}

Discriminant class: −22

∞ 2 11 a_{1} a_{2} a_{3} Over p = 2 Over p = 11 3 5 7 13 17 19 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} 3_{−} 1_{k} 0 22  1^{2} 3_{−} 2∗ 2∗ 1^{2} 1_{k} 11 11 2 2 2  2
C_{2} 2  2 2  2 2

Discriminant class: −11

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

Discriminant class: −2

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

Discriminant class: −1

∞ 2 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 3 5 7 13 17 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
5. 1_{k} 2_{i} 0_{+} 0 1  1^{2} 2_{i} −1 −1 2 0_{+} ∗ ∗ 2  2  2 2
C_{2}  2  2 2  2
6. 1_{k} 2_{i} 2_{+} -1 4 2 1^{2} 2_{i} −1 −1 1^{3} 2_{+} ∗  2 3 2 3 3 2 2 3
S_{3}  2 3 3 2 2 3 2

Discriminant class: 2

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

Discriminant class: 11

∞ 2 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11 3 5 7 13 17 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
8. 0_{+} 2_{i} 1_{k} 0 -11  1^{2} 2_{i} −∗ −∗ 1^{2} 1_{k} 11 11 2  2 2  2 2
C_{2}  2  2  2  2 2

Discriminant class: 22

∞ 2 11 a_{1} a_{2} a_{3}  Over p = 2  Over p = 11  3 5 7 13 17 19 23 29
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
9. 0_{+} 3_{k} 1_{i} 0 -22  1^{2} 3_{k} −2∗ −2∗ 1^{2} 1_{i} 11∗ 11∗  2  2 2 2
C_{2}  2 2 2 2 2 2