Properties

Label 2.25.ar_es
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:  $( 1 - 9 x + 25 x^{2} )( 1 - 8 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.204832764699$
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
$A(\F_{q^r})$ 306 364140 244698408 153113587200 95466919164066 59617302179742720 37254053386385982018 23283120527418908620800 14551911147624424677326376 9094945550432320236881846700

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 581 15660 391969 9775809 244192466 6103704105 152588258689 3814696195884 95367416254901

Decomposition

1.25.aj $\times$ 1.25.ai

Base change

This is a primitive isogeny class.