Properties

Label 2.8.af_u
Base Field $\F_{2^3}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

Learn more about

Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} )( 1 - x + 8 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.443432958871$
Angle rank:  $1$ (numerical)

Newton polygon

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

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
$A(\F_{q^r})$ 40 5200 292120 16900000 1072916200 68849762800 4399502609080 281317163400000 18009091517293960 1152907091770330000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 80 568 4128 32744 262640 2097848 16767808 134178184 1073728400

Decomposition

1.8.ae $\times$ 1.8.ab

Base change

This is a primitive isogeny class.