Properties

Label 2.25.as_fa
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:  $( 1 - 5 x )^{2}( 1 - 8 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.204832764699$
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
$A(\F_{q^r})$ 288 352512 241618464 152510791680 95367236440608 59602753904101632 37252146143642766624 23282894853620587560960 14551887191209892924290848 9094943313866324804873271552

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 8 562 15464 390430 9765608 244132882 6103391624 152586779710 3814689915848 95367392802802

Decomposition

1.25.ak $\times$ 1.25.ai

Base change

This is a primitive isogeny class.