Low Degree Fields Unramified Outside of {∞, 5, 11, 17}

Discriminant class: −935

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 11 Over p = 17 2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
1. 1_{k} 1_{−} 1_{k} 1_{+} 0 935  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{k} 11 11 1^{2} 1_{+} 17 17  2  2  2
C_{2} 28  2 2  2

Discriminant class: −187

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 17  2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
2. 1_{k} 0_{+} 1_{k} 1_{−} 0 187  2 0_{+} ∗ ∗ 1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2  2 2 2  2
C_{2} 2  2  2
3. 1_{k} 2_{+} 1_{k} 1_{−} 0 10 -5 1^{3} 2_{+} ∗  1^{2} 1_{k} 11 11 1^{2} 1_{−} 17∗ 17∗ 2 2 3 2 2 2 3 2
S_{3} 4 2 3 2 3 3 3 3

Discriminant class: −55

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 17 2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
4. 1_{k} 1_{+} 1_{i} 0_{+} 0 55  1^{2} 1_{+} 5 5 1^{2} 1_{i} 11∗ 11∗  2  2 2 2
C_{2} 4  2 2  2 2  2 2

Discriminant class: −11

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 17 2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d  s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
5. 1_{k} 0_{+} 1_{i} 0_{+} -1 3  1^{2} 1_{i} 11∗ 11∗ 2 0_{+} ∗ ∗ 2  2 2 2  2
C_{2}  2 2  2
6. 1_{k} 0_{+} 1_{i} 2_{+} -1 -11 22 3 0_{+} 1  1^{2} 1_{i} 11∗ 11∗ 1^{3} 2_{+} ∗  2 3 2 2 2 3 2
S_{3}  3 2 2 3  3 2

Discriminant class: 5

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11 Over p = 17 2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
7. 0_{+} 1_{+} 0_{+} 0_{+} 1 -1  1^{2} 1_{+} 5 5  2 0_{+} ∗ ∗ 2 2 2 2  2
C_{2}  2  2 2 2  2

Discriminant class: 17

∞ 5 11 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 11  Over p = 17 2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d s 37 41 43 47 53 59 61 67
8. 0_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗ 2 0_{+} ∗ ∗ 1^{2} 1_{+} 17 17  2 2  2 2 2
C_{2}  2 2  2
9. 0_{+} 0_{+} 2_{+} 1_{+} 0 -11 -11 2 0_{+} ∗ ∗ 1^{3} 2_{+} ∗  1^{2} 1_{+} 17 17 3 2 2 3 3 2 2 2
S_{3}  2 2 3 3  2 3

Discriminant class: 85

∞ 5 11 17 a_{1} a_{2} a_{3}  Over p = 5  Over p = 11  Over p = 17  2 3 7 13 19 23 29 31
G h  f^{e} c_{w} d s f^{e} c_{w} d s f^{e} c_{w} d  s 37 41 43 47 53 59 61 67
10. 0_{+} 1_{−} 0_{+} 1_{−} 0 -85  1^{2} 1_{−} 5∗ 5∗ 2 0_{+} ∗ ∗ 1^{2} 1_{−} 17∗ 17∗ 2  2  2 2
C_{2} 2  2 2 2 2  2 2