Properties

Label 2.4.ae_j
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:  $1-4x+9x^{2}-16x^{3}+16x^{4}$
Frobenius angles:  $\pm0.117169895439$, $\pm0.478661301576$
Angle rank:  $2$ (numerical)
Number field:  4.0.4752.1
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
$A(\F_{q^r})$ 6 276 3942 57408 1046166 17589204 273933078 4298940672 68831612838 1103041860756

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 1 19 61 223 1021 4291 16717 65599 262573 1051939

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.