Properties

Label 2.4.ab_i
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:  $(1-x+4x^{2})(1+4x^{2})$
Frobenius angles:  $\pm0.419569376745$, $\pm0.5$
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
$A(\F_{q^r})$ 20 600 4940 54000 988100 17339400 272580860 4276044000 68515265780 1099903515000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 4 32 76 208 964 4232 16636 65248 261364 1048952

Decomposition

1.4.ab $\times$ 1.4.a

Base change

This is a primitive isogeny class.