Low Degree Fields Unramified Outside of {∞, 7, 37}

Discriminant class: −259

∞ 7 37 a_{1} a_{2} a_{3} Over p = 7 Over p = 37 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
1. 1_{k} 1_{i} 1_{+} 0 259  1^{2} 1_{i} 7∗ 7∗ 1^{2} 1_{+} 37 37 2 2  2
C_{2} 4  2  2 2 2

Discriminant class: −7

∞ 7 37 a_{1} a_{2} a_{3} Over p = 7 Over p = 37 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
2. 1_{k} 1_{i} 0_{+} 1 2  1^{2} 1_{i} 7∗ 7∗  2 2  2 2 2
C_{2}  2 2  2  2 2
3. 1_{k} 1_{i} 2_{+} -1 -12 63 1^{2} 1_{i} 7∗ 7∗ 1^{3} 2_{+} 1  3 2 2 3 2 2 2 3
S_{3} 3 3 2 2 2 3 2 2

Discriminant class: 1

∞ 7 37 a_{1} a_{2} a_{3} Over p = 7  Over p = 37 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
4. 0_{+} 2_{+} 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
5. 0_{+} 0_{+} 2_{+} 1 -12 11 3 0_{+} 1  1^{3} 2_{+} 1  3 3 3  3 3 3
C_{3}  3  3 3 3
6. 0_{+} 2_{+} 2_{+} 1 -86 48 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3 3 3 3 3
C_{3} 3  3 3  3 3 3 3
7. 0_{+} 2_{+} 2_{+} -1 -86 211 1^{3} 2_{+} 1  1^{3} 2_{+} 1  3 3  3 3  3
C_{3} 3  3 3  3

Discriminant class: 37

∞ 7 37 a_{1} a_{2} a_{3} Over p = 7  Over p = 37 2 3 5 11 13 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 41 43 47 53 59 61
8. 0_{+} 0_{+} 1_{+} 0 -37  1^{2} 1_{+} 37 37 2  2  2 2 2 2
C_{2}  2 2  2  2 2