Properties

Label 2.25.an_di
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 25 x^{2} )( 1 - 4 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.369010119566$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 374 392700 247003064 152738308800 95352068016854 59605593789772800 37254102630810524294 23283288692250362899200 14551932224923307126219384 9094946344199137539057517500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 629 15808 391009 9764053 244144514 6103712173 152589360769 3814701721168 95367424578149

Decomposition

1.25.aj $\times$ 1.25.ae

Base change

This is a primitive isogeny class.