Low Degree Fields Unramified Outside of {∞, 11, 17, 23}

Discriminant class: −391

∞ 11 17 23 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  Over p = 23 2 3 5 7 13 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} 0_{+} 1_{−} 1_{k} 0 391  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23  2  2 2 2
C_{2} 14  2 2  2  2

Discriminant class: −187

∞ 11 17 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 23 2 3 5 7 13 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
2. 1_{k} 1_{k} 1_{−} 0_{+} 0 187  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗ 2 2 2  2 2  2
C_{2} 2  2  2
3. 1_{k} 1_{k} 1_{−} 2_{+} 0 -92 -345 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  2 2 2 3 2 2 3 2
S_{3} 2 2 2 3 3 3

Discriminant class: −23

∞ 11 17 23 a_{1} a_{2}  a_{3} Over p = 11 Over p = 17  Over p = 23  2 3 5 7 13 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
4. 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
5. 1_{k} 0_{+} 0_{+} 1_{i} -1  0  1 2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2 3 3
S_{3}  2 3 2 3 2  2 2
6. 1_{k} 2_{+} 2_{+} 1_{i} -1 -62 -1032 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗  2 2 3 2 3 3
S_{3} 3  2 3 2  2 3 2 2
7. 1_{k} 2_{+} 2_{+} 1_{i} -1 -62 277 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2 3 2  3
S_{3} 3  2 3 2 3 2 3 2 2
8. 1_{k} 2_{+} 2_{+} 1_{i} 0 -187 -1309 1^{3} 2_{+} ∗  1^{3} 2_{+} ∗  1^{2} 1_{i} 23∗ 23∗ 3 3 2 2  2 3
S_{3} 3  2  2 3 2 3 2 2

Discriminant class: −11

∞ 11 17 23 a_{1} a_{2} a_{3}  Over p = 11  Over p = 17 Over p = 23 2 3 5 7 13 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
9. 1_{k} 1_{i} 0_{+} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗  2  2 2 2 2
C_{2}  2 2  2
10. 1_{k} 1_{i} 2_{+} 0_{+} -1 -11 22 1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  3 0_{+} 1  2 3 3 2 2 2 2
S_{3}  3 2 2 3  3 2

Discriminant class: 17

∞ 11 17 23 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  Over p = 23 2 3 5 7 13 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_{+} 0_{+} 1_{+} 0_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2  2 2
C_{2}  2 2  2
12. 0_{+} 2_{+} 1_{+} 0_{+} 0 -11 -11 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗ 3 2 2 2 3 3 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 253

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

Discriminant class: 4301

∞ 11 17 23 a_{1}  a_{2} a_{3}  Over p = 11  Over p = 17  Over p = 23 2 3 5 7 13 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
14. 0_{+} 1_{i} 1_{+} 1_{k} 0 -4301  1^{2} 1_{i} 11∗ 11∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 2 2  2 2  2
C_{2} 2  2  2 2