Properties

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

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Invariants

Base field:  $\F_{2^3}$
Dimension:  $2$
Weil polynomial:  $( 1 - 4 x + 8 x^{2} )( 1 + x + 8 x^{2} )$
Frobenius angles:  $\pm0.25$, $\pm0.556567041129$
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
$A(\F_{q^r})$ 50 5200 267050 16900000 1091476250 68849762800 4388008863050 281317163400000 18015307991997050 1152907091770330000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 6 80 522 4128 33306 262640 2092362 16767808 134224506 1073728400

Decomposition

1.8.ae $\times$ 1.8.b

Base change

This is a primitive isogeny class.