Properties

Label 2.25.ar_eq
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x )^{2}( 1 - 7 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.253183311107$
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
$A(\F_{q^r})$ 304 361152 243063808 152586720000 95347337072944 59596558408138752 37251229473994725808 23282826329038573440000 14551890780248881319762944 9094945341050872863732418752

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 577 15558 390625 9763569 244107502 6103241433 152586330625 3814690856694 95367414059377

Decomposition

1.25.ak $\times$ 1.25.ah

Base change

This is a primitive isogeny class.