Low Degree Fields Unramified Outside of {∞, 5, 11, 23}

Discriminant class: −115

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5 Over p = 11 Over p = 23 2 3 7 13 17 19 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} 1_{−} 0_{+} 1_{k} 0 115  1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 1^{2} 1_{k} 23 23 2 2  2  2
C_{2} 2  2  2
2. 1_{k} 1_{−} 2_{+} 1_{k} -1 15 2 1^{2} 1_{−} 5∗ 5∗ 1^{3} 2_{+} ∗  1^{2} 1_{k} 23 23 2 2 3 2  2 3 3
S_{3}  3  3 2 3  2 3

Discriminant class: −55

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 23 2 3 7 13 17 19 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} 1_{+} 1_{i} 0_{+} 0 55  1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗  2  2 2
C_{2} 4  2 2  2 2  2 2
4. 1_{k} 1_{+} 1_{i} 2_{+} 0 -23 -138 1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 3 3 2 2 3
S_{3}  2 2 3 2 2 3 2 2

Discriminant class: −23

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 23  2 3 7 13 17 19 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. 1_{k} 0_{+} 0_{+} 1_{i} 0 23  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗  2  2 2
C_{2} 3  2  2  2  2 2
6. 1_{k} 0_{+} 0_{+} 1_{i} -1 0  1 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 3 3 2 3 2 2 3 3
S_{3}  2 3 2 3 2  2 2
7. 1_{k} 2_{+} 2_{+} 1_{i} -1 -18 -53 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 3 2 2  3
S_{3} 3  2 3 2 3 2 3 2 2
8. 1_{k} 2_{+} 2_{+} 1_{i} 0 -55 -165 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3  2 3 2 2 3
S_{3} 3  2  2 3 2 3 2 2
9. 1_{k} 2_{+} 2_{+} 1_{i} -1 -18 112 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  3 2  2 2 3 3
S_{3} 3  2 3 2  2 3 2 2

Discriminant class: −11

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 23 2 3 7 13 17 19 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
10. 1_{k} 0_{+} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗  2  2 2 2 2 2
C_{2}  2 2  2

Discriminant class: 5

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 11 Over p = 23 2 3 7 13 17 19 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
11. 0_{+} 1_{+} 0_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5  2 0_{+} ∗ ∗ 2 2 2 2 2
C_{2}  2  2 2 2  2

Discriminant class: 253

∞ 5 11 23 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 23  2 3 7 13 17 19 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
12. 0_{+} 0_{+} 1_{k} 1_{i} 0 -253  2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 1^{2} 1_{i} 23∗ 23∗ 2  2  2
C_{2}  2 2  2  2

Discriminant class: 1265

∞ 5 11 23 a_{1}  a_{2} a_{3}  Over p = 5  Over p = 11  Over p = 23 2 3 7 13 17 19 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
13. 0_{+} 1_{−} 1_{k} 1_{k} 0 -1265 1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11 1^{2} 1_{k} 23 23 2 2 2 2
C_{2} 2  2 2 2