Properties

Label 3.4.ah_ba_acm
Base Field $\F_{2^2}$
Dimension $3$
$p$-rank $1$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{2^2}$
Dimension:  $3$
Weil polynomial:  $( 1 - 2 x )^{2}( 1 - 2 x + 4 x^{2} )( 1 - x + 4 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.333333333333$, $\pm0.419569376745$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1/2, 1/2, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 12 4536 301644 14742000 919919172 64650151944 4362111469308 281333762892000 17960660287880436 1149959015483709816

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 20 76 224 868 3848 16252 65504 261364 1045880

Decomposition

1.4.ae $\times$ 1.4.ac $\times$ 1.4.ab

Base change

This is a primitive isogeny class.