Low Degree Fields Unramified Outside of {∞, 17, 41}

Discriminant class: 17

∞ 17 41 a_{1} a_{2} a_{3} Over p = 17 Over p = 41 2 3 5 7 11 13 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_{+} 1_{+} 0_{+} 1 -4  1^{2} 1_{+} 17 17 2 0_{+} ∗ ∗  2 2 2 2  2
C_{2}  2 2 2  2

Discriminant class: 41

∞ 17 41 a_{1} a_{2} a_{3} Over p = 17  Over p = 41 2 3 5 7 11 13 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_{+} 0_{+} 1_{+} 0 -41  2 0_{+} ∗ ∗ 1^{2} 1_{+} 41 41  2  2 2 2 2
C_{2}  2  2 2
3. 0_{+} 2_{+} 1_{+} 0 -17 -17 1^{3} 2_{+} ∗  1^{2} 1_{+} 41 41 3 2 3 2 2 2 2
S_{3} 2 3 3 2 2 3 3

Discriminant class: 697

∞ 17 41 a_{1} a_{2} a_{3}  Over p = 17  Over p = 41  2 3 5 7 11 13 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_{+} 1_{−} 1_{−} 0 -697  1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 41∗ 41∗  2  2 2 2
C_{2} 6  2 2  2 2  2
5. 0_{+} 1_{−} 1_{−} 0 -7 -5 1^{2} 1_{−} 17∗ 17∗ 1^{2} 1_{−} 41∗ 41∗ 3 3 2 3  2 2 2
S_{3}  3 2 2 3 2 2 3 2