Properties

Label 2.25.ap_ec
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 8 x + 25 x^{2} )( 1 - 7 x + 25 x^{2} )$
Frobenius angles:  $\pm0.204832764699$, $\pm0.253183311107$
Angle rank:  $2$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 342 383724 248406912 153489600000 95469283953702 59609926469643264 37252379952251175942 23282895234936902400000 14551892545392071418736512 9094945362477646373140130604

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 613 15896 392929 9776051 244162258 6103429931 152586782209 3814691319416 95367414284053

Decomposition

1.25.ai $\times$ 1.25.ah

Base change

This is a primitive isogeny class.