Properties

Label 2.4.ad_i
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 3 x + 4 x^{2} )( 1 + 4 x^{2} )$
Frobenius angles:  $\pm0.230053456163$, $\pm0.5$
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
$A(\F_{q^r})$ 10 400 4810 64800 1109050 17508400 267042730 4232347200 68458118170 1100399410000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 24 74 256 1082 4272 16298 64576 261146 1049424

Decomposition

1.4.ad $\times$ 1.4.a

Base change

This is a primitive isogeny class.