Low Degree Fields Unramified Outside of {∞, 5, 7}

Discriminant class: −35

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5 Over p = 7 2 3 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} 1_{−} 1_{k} 0 35  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 7 7 2  2 2
C_{2} 2  2 2 2 2  2 2 2

Discriminant class: −7

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

Discriminant class: 1

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

∞ 5 7 a_{1} a_{2} a_{3} Over p = 5  Over p = 7 2 3 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_{+} 1_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5 2 0_{+} ∗ ∗ 2 2  2 2  2
C_{2}  2  2 2 2