Low Degree Fields Unramified Outside of {∞, 7, 17, 23}

Discriminant class: −391

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23 2 3 5 11 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
2. 1_{k} 2_{+} 1_{−} 1_{k} 0 7 -133 1^{3} 2_{+} 1  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{k} 23 23 3 2  3 3 2 2 2
S_{3} 3  2 2  2 3 3 2

Discriminant class: −119

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23 2 3 5 11 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
3. 1_{k} 1_{k} 1_{−} 0_{+} 0 119  1^{2} 1_{k} 7 7 1^{2} 1_{−} 17∗ 17∗ 2 0_{+} ∗ ∗  2 2 2 2
C_{2} 10  2  2  2
4. 1_{k} 1_{k} 1_{−} 2_{+} 0 23 -23 1^{2} 1_{k} 7 7 1^{2} 1_{−} 17∗ 17∗ 1^{3} 2_{+} ∗  3 3 3 2 2 2 2
S_{3} 5  2 3 3 2 3 2 3 3

Discriminant class: −23

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23  2 3 5 11 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
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 2 3 2 3 3
S_{3} 2 3 2 3 2 2 2

Discriminant class: −7

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7 Over p = 17 Over p = 23 2 3 5 11 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
7. 1_{k} 1_{i} 0_{+} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗ 2 0_{+} ∗ ∗  2 2  2 2  2
C_{2}  2  2  2 2
8. 1_{k} 1_{i} 2_{+} 0_{+} -1 6 5 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} ∗  3 0_{+} 1  3 2 2  2 2 3 2
S_{3}  3 2 3 2 3 2 2

Discriminant class: 1

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

Discriminant class: 17

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23 2 3 5 11 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
10. 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

Discriminant class: 161

∞ 7 17 23 a_{1} a_{2} a_{3} Over p = 7  Over p = 17  Over p = 23  2 3 5 11 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_{+} 1_{k} 0_{+} 1_{i} 0 -161  1^{2} 1_{k} 7 7  1^{2} 1_{i} 23∗ 23∗  2  2 2  2
C_{2}  2 2 2 2 2 2  2

Discriminant class: 2737

∞ 7 17 23 a_{1}  a_{2} a_{3}  Over p = 7  Over p = 17  Over p = 23 2 3 5 11 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
12. 0_{+} 1_{i} 1_{+} 1_{k} 0 -2737 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 17 17 1^{2} 1_{k} 23 23 2 2 2
C_{2} 2  2 2 2 2 2 2