Quartic Fields Unramified Outside of {∞, 11, 17}

Discriminant class: 1

∞ 11 17 a_{1} a_{2} a_{3} Over p = 11  Over p = 17 2 3 5 7 13 19 23 29
G h a_{4} f^{e} c_{w} d s f^{e} c_{w} d s 31 37 41 43 47 53 59 61
1. 2_{−} 2_{+} 2_{−} 0 -3 0 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V 22 22 22 22 22 22 22 22
V_{4} 49 22 22 22 22 22

Discriminant class: 17

∞ 11 17 a_{1} a_{2} a_{3} Over p = 11  Over p = 17  2 3 5 7 13 19 23 29
G h  a_{4}  f^{e} c_{w} d s f^{e} c_{w} d  s 31 37 41 43 47 53 59 61
2. 0_{+} 0_{+} 3_{+} 1 -6 -1 4 0_{+} ∗ ∗ 1^{4} 3_{+} 17 17 22 4 4 4  22 4 4
C_{4}  1  4 4 4 22  22 22 4
3. 2_{−} 2_{−} 3_{+} 1 45 -1 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{+} 17 17  4 4 4 22  4 4
C_{4} 34  562  4 4 4  22 22 4
4. 2_{−} 2_{+} 1_{−} -1 0 3 1^{3} 2_{+} ∗  1^{2} 1_{−} 17∗ 17∗ 3 4 2 4 3 3 4 4
S_{4}  2  2 0_{+} ∗  ∗ 2 4 4 3 3 22 22 4