Properties

Label 2.4.ad_k
Base Field $\F_{2^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

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

Newton polygon

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

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 12 504 6156 65520 957252 16288776 270451452 4326547680 68782902516 1098831485304

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 2 28 92 256 932 3976 16508 66016 262388 1047928

Decomposition

1.4.ac $\times$ 1.4.ab

Base change

This is a primitive isogeny class.