Properties

Label 3.4.ah_bc_acq
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:  $( 1 - 3 x + 4 x^{2} )( 1 - 2 x + 4 x^{2} )^{2}$
Frobenius angles:  $\pm0.230053456163$, $\pm0.333333333333$, $\pm0.333333333333$
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
$A(\F_{q^r})$ 18 7056 485514 21464352 1066905018 65280270384 4307399218602 281747652443712 18086429445114906 1153854610392906576

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 24 106 320 1018 3888 16042 65600 263194 1049424

Decomposition

1.4.ad $\times$ 1.4.ac 2

Base change

This is a primitive isogeny class.