Low Degree Fields Unramified Outside of {∞, 3, 17}

Discriminant class: −51

∞ 3 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 17  2 5 7 11 13 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_{k} 1_{−} 0 51  1^{2} 1_{k} 3 3 1^{2} 1_{−} 17∗ 17∗ 2  2
C_{2} 2  2 2  2 2 2 2
2. 1_{k} 3_{k} 1_{−} 0 3 -8 1^{3} 3_{k} 3  1^{2} 1_{−} 17∗ 17∗ 2 3 2  3 3 3 3
S_{3}  2 2 3 3 2 2 2 2

Discriminant class: −3

∞ 3 17 a_{1} a_{2} a_{3} Over p = 3 Over p = 17 2 5 7 11 13 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 0_{+} ∗ ∗ 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∗  2 0_{+} ∗ ∗ 2 2 3 2 3 3 2 2
S_{3}  3 3 2 3 2 2 2
5. 1_{k} 1_{i} 2_{+} -1 6 -12 1^{2} 1_{i} 3∗ 3∗ 1^{3} 2_{+} ∗  2 2 3 2 3 3 2 2
S_{3}  3 3 2 3 2 2 2 3
6. 1_{k} 5_{i} 2_{+} 0 0 -51 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2 3 2  3 2 2
S_{3} 3  3  2  2 2 2 3
7. 1_{k} 5_{i} 2_{+} 0 0 -153 1^{3} 5_{i} 3∗  1^{3} 2_{+} ∗  2 2  2 3  2 2
S_{3} 9  3 2 3 2 2 2 3

Discriminant class: 1

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

Discriminant class: 17

∞ 3 17 a_{1} a_{2} a_{3} Over p = 3  Over p = 17 2 5 7 11 13 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
9. 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2 2  2 2
C_{2}  2 2 2  2