Properties

Label 2.4.ab_c
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:  $( 1 - 3 x + 4 x^{2} )( 1 + 2 x + 4 x^{2} )$
Frobenius angles:  $\pm0.230053456163$, $\pm0.666666666667$
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
$A(\F_{q^r})$ 14 336 3626 78624 1143674 16447536 269128874 4282334784 68190704666 1099326896976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 20 58 304 1114 4016 16426 65344 260122 1048400

Decomposition

1.4.ad $\times$ 1.4.c

Base change

This is a primitive isogeny class.