Quartic Fields Unramified Outside of {∞, 5, 17}

Discriminant class: 1

∞ 5 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 2 3 7 11 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. 0_{+} 2_{−} 2_{−} 0 -11 0 2^{2} 2_{−} 1 V 2^{2} 2_{−} 1 V 22 22 22 22 22  22 22
V_{4} 9 22 22 22 22 22 22 22

Discriminant class: 5

∞ 5 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 2 3 7 11 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. 2_{−} 3_{−} 0_{+} -1 1 -1 1^{4} 3_{−} 5 5 4 0_{+} ∗ ∗ 4 4 4  4 22 4 22
C_{4} 1 4 4 4 4 22
3. 2_{−} 3_{−} 2_{+} -1 21 -21 1^{4} 3_{−} 5 5 2^{2} 2_{+} ∗ ∗ 4 4 4 22 4 22 4
C_{4} 2 101 22 4 22 4 4 4 22 22

Discriminant class: 17

∞ 5 17 a_{1} a_{2} a_{3} Over p = 5  Over p = 17 2 3 7 11 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
4. 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
5. 0_{+} 2_{+} 3_{+} -1 -23 1 2^{2} 2_{+} ∗ ∗ 1^{4} 3_{+} 17 17  4 4 4 22 22 4 4
C_{4} 2 86 4 4 4 22 22 4

Discriminant class: 85

∞ 5 17 a_{1} a_{2} a_{3}  Over p = 5  Over p = 17  2 3 7 11 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
6. 2_{−} 3_{+} 3_{−} 1 11 -69 1^{4} 3_{+} 5∗ 5∗ 1^{4} 3_{−} 17∗ 17∗ 4 22 22 4 4  4
C_{4} 4  171  4  4 4 4 4  4
7. 2_{−} 3_{+} 3_{−} 1 11 101 1^{4} 3_{+} 5∗ 5∗ 1^{4} 3_{−} 17∗ 17∗ 4  4 4  22 4
C_{4} 20  171  4 22 4 4 4 4  4