Properties

Label 2.13.ah_bb
Base Field $\F_{13}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{13}$
Dimension:  $2$
Weil polynomial:  $1 - 7 x + 27 x^{2} - 91 x^{3} + 169 x^{4}$
Frobenius angles:  $\pm0.100578918488$, $\pm0.493559382189$
Angle rank:  $2$ (numerical)
Number field:  4.0.6525.1
Galois group:  $D_4$

This isogeny class is simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains a Jacobian, and hence is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 99 29205 4723191 803283525 137817648144 23325927456645 3938111380279791 665408712724467525 112457099369691216459 19005166413893781792000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 175 2149 28123 371182 4832575 62760229 815721043 10604658967 137859961750

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.