Properties

Label 2.25.ao_dm
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:  $( 1 - 5 x )^{2}( 1 - 4 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.369010119566$
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
$A(\F_{q^r})$ 352 380160 243894112 152136990720 95252505216352 59591048371303680 37252195385546212192 23283063016822088663040 14551908268474076390753632 9094944107632946909412844800

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 610 15612 389470 9753852 244084930 6103399692 152587881790 3814695441132 95367401126050

Decomposition

1.25.ak $\times$ 1.25.ae

Base change

This is a primitive isogeny class.