Properties

Label 2.4.ab_h
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $1-x+7x^{2}-4x^{3}+16x^{4}$
Frobenius angles:  $\pm0.36744260714$, $\pm0.549379399016$
Angle rank:  $2$ (numerical)
Number field:  4.0.5225.1
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
$A(\F_{q^r})$ 19 551 4636 60059 1036849 16671056 265686139 4317100979 69137924356 1098436793751

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 30 73 234 1014 4071 16216 65874 263737 1047550

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.