Low Degree Fields Unramified Outside of {∞, 13, 41}

Discriminant class: 1

∞ 13 41 a_{1} a_{2} a_{3} Over p = 13 Over p = 41 2 3 5 7 11 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 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 41 a_{1} a_{2} a_{3} Over p = 13 Over p = 41 2 3 5 7 11 17 19 23
G h  f^{e} c_{w} d s f^{e} c_{w} d s 29 31 37 43 47 53 59 61
2. 0_{+} 1_{+} 0_{+} 1 -3  1^{2} 1_{+} 13 13 2 0_{+} ∗ ∗ 2  2 2 2  2
C_{2}  2 2  2  2
3. 0_{+} 1_{+} 2_{+} -1 -27 -38 1^{2} 1_{+} 13 13 1^{3} 2_{+} ∗  2 3 2 2 2 3 2 3
S_{3} 3 2 2 3 2 2

Discriminant class: 41

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

Discriminant class: 533

∞ 13 41 a_{1} a_{2} a_{3}  Over p = 13  Over p = 41  2 3 5 7 11 17 19 23
G h  f^{e} c_{w} d  s f^{e} c_{w} d  s 29 31 37 43 47 53 59 61
5. 0_{+} 1_{−} 1_{−} 0 -533  1^{2} 1_{−} 13∗ 13∗ 1^{2} 1_{−} 41∗ 41∗ 2 2 2  2
C_{2} 2  2 2 2  2 2