Quartic Fields Unramified Outside of {∞, 7, 17}

Discriminant class: 1

∞ 7 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 17 2 3 5 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. 2_{−} 2_{+} 2_{−} 0 -5 0 2^{2} 2_{+} 1 V 2^{2} 2_{−} 1 V  22 22 22 22 22 22 22
V_{4} 5 36 22 22 22 22 22 22

Discriminant class: 17

∞ 7 17 a_{1} a_{2} a_{3} Over p = 7  Over p = 17 2 3 5 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. 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 28 1 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{+} 17 17 22 4 4 4 22  4 4
C_{4} 2  239  4 4 4 22 22 22  4