Quartic Fields Unramified Outside of {∞, 7, 13}

Discriminant class: 1

∞ 7 13 a_{1} a_{2} a_{3} Over p = 7  Over p = 13 2 3 5 11 17 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
V_{4} 25 22 22 22 22 22 22
2. 2_{−} 2_{+} 2_{−} -1 5 -4 1^{3} 2_{+} 1  2^{2} 2_{−} 1 V 3 3 3 3 3 3 3 22
A_{4} 2 3 3 3 22 22 3 3 3 3

Discriminant class: 13

∞ 7 13 a_{1} a_{2} a_{3} Over p = 7  Over p = 13 2 3 5 11 17 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
3. 2_{−} 0_{+} 3_{−} -1 2 4 4 0_{+} ∗ ∗ 1^{4} 3_{−} 13 13 4  4 4 22 4 22
C_{4} 3 4 4 4 22 4 4
4. 0_{+} 2_{−} 3_{−} 1 -24 22 2^{2} 2_{−} ∗ ∗ 1^{4} 3_{−} 13 13 4 22 4 4  4 22
C_{4}  29  4 4 4 22 4  4 22