Low Degree Fields Unramified Outside of {∞, 5, 13, 17}

Discriminant class: 1

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

Discriminant class: 5

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

Discriminant class: 13

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

Discriminant class: 17

∞ 5 13 17 a_{1} a_{2} a_{3} Over p = 5 Over p = 13 Over p = 17 2 3 7 11 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. 0_{+} 0_{+} 0_{+} 1_{+} 1 -4  2 0_{+} ∗ ∗  1^{2} 1_{+} 17 17  2 2 2  2 2 2
C_{2}  2 2  2
5. 0_{+} 2_{+} 2_{+} 1_{+} 0 -65 -195 1^{3} 2_{+} ∗  1^{3} 2_{+} 1  1^{2} 1_{+} 17 17 3 2 2 2 3 2 2 2
S_{3} 3  2 2 3 3 3 3 2 3

Discriminant class: 65

∞ 5 13 17 a_{1} a_{2} a_{3}  Over p = 5  Over p = 13  Over p = 17 2 3 7 11 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
6. 0_{+} 1_{−} 1_{−} 0_{+} 0 -65  1^{2} 1_{−} 5∗ 5∗ 1^{2} 1_{−} 13∗ 13∗ 2 0_{+} ∗ ∗  2  2 2 2  2
C_{2} 2  2 2  2 2

Discriminant class: 85

∞ 5 13 17 a_{1} a_{2} a_{3}  Over p = 5  Over p = 13  Over p = 17  2 3 7 11 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_{+} 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

Discriminant class: 221

∞ 5 13 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 13  Over p = 17 2 3 7 11 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_{+} 1_{+} 1_{+} 0 -221  1^{2} 1_{+} 13 13 1^{2} 1_{+} 17 17 2 2  2 2 2
C_{2} 2  2  2 2 2

Discriminant class: 1105

∞ 5 13 17 a_{1}  a_{2} a_{3} Over p = 5  Over p = 13  Over p = 17  2 3 7 11 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
9. 0_{+} 1_{+} 1_{−} 1_{−} 0 -1105  1^{2} 1_{+} 5 5 1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 17∗ 17∗  2  2  2
C_{2} 4  2  2  2 2 2