Properties

Label 2.25.ap_ea
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:  $( 1 - 9 x + 25 x^{2} )( 1 - 6 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.295167235301$
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
$A(\F_{q^r})$ 340 380800 246971920 153113587200 95410665939700 59605823308595200 37252923389200408180 23283120527418908620800 14551931318543043402649360 9094949232869223952579120000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 11 609 15806 391969 9770051 244145454 6103518971 152588258689 3814701483566 95367454868049

Decomposition

1.25.aj $\times$ 1.25.ag

Base change

This is a primitive isogeny class.