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

Discriminant class: 1

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

Discriminant class: 13

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

Discriminant class: 17

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

Discriminant class: 221

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