Properties

Label 2.8.aj_bj
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $1 - 9 x + 35 x^{2} - 72 x^{3} + 64 x^{4}$
Frobenius angles:  $\pm0.0373126015494$, $\pm0.296020731784$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}, \sqrt{5})\)
Galois group:  $V_4$

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
$A(\F_{q^r})$ 19 3439 261364 16744491 1064657989 68311140496 4387996235719 281338409363859 18014398647305836 1152964013465503999

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 0 54 513 4090 32490 260583 2092356 16769074 134217729 1073781414

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.