Low Degree Fields Unramified Outside of {∞, 3, 7}

Discriminant class: −7

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

Discriminant class: −3

∞ 3 7 a_{1} a_{2} a_{3} Over p = 3 Over p = 7 2 5 11 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
3. 1_{k} 1_{i} 0_{+} 1 1  1^{2} 1_{i} 3∗ 3∗  2 2 2  2  2 2
C_{2}  2  2 2 2
4. 1_{k} 5_{i} 0_{+} 0 0 -3 1^{3} 5_{i} 3∗  3 0_{+} 1  2 2 2 3 2 3 2 2
S_{3}  3 3 2 3 2 2 2
5. 1_{k} 3_{i} 2_{+} 0 0 -7 1^{3} 3_{i} 3∗ 1^{3} 2_{+} 1 2 2 2 3 2 2 2
S_{3} 3  3 3 2 3 2 2 2 3
6. 1_{k} 5_{i} 2_{+} 0 0 -21 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 2  2 3 2 2
S_{3} 3  3 3 2  2 2 2 3
7. 1_{k} 5_{i} 2_{+} 0 0 -63 1^{3} 5_{i} 3∗  1^{3} 2_{+} 1  2 2 2 3 2 3 2 2
S_{3} 6  2 3 2 2 2 3

Discriminant class: 1

∞ 3 7 a_{1} a_{2} a_{3} Over p = 3  Over p = 7 2 5 11 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_{+} 0_{+} 2_{+} -1 -2 1 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3 3  3 3 3 3
9. 0_{+} 4_{+} 0_{+} 0 -3 1 1^{3} 4_{+} 1  3 0_{+} 1  3 3 3 3  3 3
C_{3}  3  3 3 3  3 3
10. 0_{+} 4_{+} 2_{+} 0 -21 -28 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3 3
C_{3} 3  3 3 3  3
11. 0_{+} 4_{+} 2_{+} 0 -21 35 1^{3} 4_{+} 1  1^{3} 2_{+} 1  3  3 3 3  3
C_{3} 3  3 3 3 3 3 3 3 3

Discriminant class: 21

∞ 3 7 a_{1} a_{2} a_{3} Over p = 3 Over p = 7 2 5 11 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
12. 0_{+} 1_{k} 1_{i} 0 -21  1^{2} 1_{k} 3 3 1^{2} 1_{i} 7∗ 7∗ 2  2 2  2 2 2
C_{2}  2  2  2