Properties

Label 2.2.b_a
Base Field $\F_{2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2}$
Dimension:  $2$
Weil polynomial:  $1 + x + 2 x^{3} + 4 x^{4}$
Frobenius angles:  $\pm0.313829601922$, $\pm0.860613258134$
Angle rank:  $2$ (numerical)
Number field:  4.0.2312.1
Galois group:  $D_{4}$

This isogeny class is simple.

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
$A(\F_{q^r})$ 8 16 152 416 808 3952 11768 74048 265544 1132816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 4 16 24 24 64 88 288 520 1104

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.