Low Degree Fields Unramified Outside of {∞, 2, 7}

Discriminant class: −14

∞ 2 7 a_{1} a_{2} a_{3} Over p = 2 Over p = 7 3 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} 3_{+} 1_{i} 0 14 1^{2} 3_{+} 2 2 1^{2} 1_{i} 7∗ 7∗ 2 2 2
C_{2} 4  2 2 2 2 2 2

Discriminant class: −7

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

Discriminant class: −2

∞ 2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 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} 3_{i} 0_{+} 0 2  1^{2} 3_{i} −2 −2 2 0_{+} ∗ ∗  2  2  2 2
C_{2}  2 2  2 2  2

Discriminant class: −1

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

Discriminant class: 1

∞ 2 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 7 3 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
5. 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

Discriminant class: 2

∞ 2 7 a_{1} a_{2} a_{3} Over p = 2  Over p = 7 3 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
6. 0_{+} 3_{+} 0_{+} 0 -2  1^{2} 3_{+} 2 2  2 2 2 2  2  2
C_{2}  2  2  2 2 2

Discriminant class: 7

∞ 2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 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
7. 0_{+} 2_{i} 1_{k} 0 -7  1^{2} 2_{i} −1 −1 1^{2} 1_{k} 7 7  2 2 2 2  2
C_{2}  2 2  2

Discriminant class: 14

∞ 2 7 a_{1} a_{2} a_{3}  Over p = 2  Over p = 7 3 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_{+} 3_{i} 1_{k} 0 -14  1^{2} 3_{i} −2 −2 1^{2} 1_{k} 7 7 2  2 2 2 2
C_{2}  2 2  2 2