Low Degree Fields Unramified Outside of {∞, 7, 13, 17}

Discriminant class: −1547

∞ 7 13 17 a_{1} a_{2} a_{3}  Over p = 7  Over p = 13  Over p = 17  2 3 5 11 19 23 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_{i} 1_{−} 1_{−} 0 1547  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 17∗ 17∗ 2  2  2 2 2
C_{2} 12  2  2
2. 1_{k} 1_{i} 1_{−} 1_{−} -1  -1 8 1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 17∗ 17∗ 2 3 2 3 3 2 2 2
S_{3} 3 2 3 3 3 2

Discriminant class: −119

∞ 7 13 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 17  2 3 5 11 19 23 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} 0_{+} 1_{−} 0 119  1^{2} 1_{k} 7 7 2 0_{+} ∗ ∗ 1^{2} 1_{−} 17∗ 17∗  2 2 2 2
C_{2} 10  2  2  2

Discriminant class: −91

∞ 7 13 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 17 2 3 5 11 19 23 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} 1_{k} 1_{−} 0_{+} 0 91  1^{2} 1_{k} 7 7 1^{2} 1_{−} 13∗ 13∗ 2 0_{+} ∗ ∗ 2 2  2
C_{2} 2  2  2 2
5. 1_{k} 1_{k} 1_{−} 2_{+} 0 -17 -68 1^{2} 1_{k} 7 7 1^{2} 1_{−} 13∗ 13∗ 1^{3} 2_{+} ∗  2 2 3 2 3  3 3
S_{3}  2 3 3  3 2 2

Discriminant class: −7

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

Discriminant class: 1

∞ 7 13 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 13 Over p = 17 2 3 5 11 19 23 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
8. 0_{+} 2_{+} 0_{+} 0_{+} -1 -2 1 1^{3} 2_{+} 1  3 0_{+} 1  3 3 3 3 3 3  3
C_{3}  3  3 3 3 3 3
9. 0_{+} 0_{+} 2_{+} 0_{+} -1 -4 -1 3 0_{+} 1  1^{3} 2_{+} 1  3 0_{+} 1  3 3  3 3 3 3
C_{3}  3 3 3  3 3 3
10. 0_{+} 2_{+} 2_{+} 0_{+} -1 -30 64 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3  3 3
C_{3} 3  3 3 3 3  3 3

Discriminant class: 1 (continued)

∞ 7 13 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 13 Over p = 17 2 3 5 11 19 23 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_{+} 2_{+} 2_{+} 0_{+} 1 -30 27 1^{3} 2_{+} 1 1^{3} 2_{+} 1 3 0_{+} 1 3 3 3 3 3
C_{3} 3  3 3 3 3 3 3

Discriminant class: 13

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

Discriminant class: 17

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

Discriminant class: 221

∞ 7 13 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 13  Over p = 17 2 3 5 11 19 23 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_{+} 0_{+} 1_{+} 1_{+} 0 -221  1^{2} 1_{+} 13 13 1^{2} 1_{+} 17 17 2 2  2 2 2
C_{2} 2  2  2 2 2