Properties

Label 2.25.an_dc
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:  $( 1 - 5 x )^{2}( 1 - 3 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.403013315979$
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
$A(\F_{q^r})$ 368 384192 243309824 151932568320 95245488225008 59595074223132672 37252756265962788464 23283036020347762314240 14551894533235760914496768 9094943300779531678164149952

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 617 15574 388945 9753133 244101422 6103491589 152587704865 3814691840518 95367392665577

Decomposition

1.25.ak $\times$ 1.25.ad

Base change

This is a primitive isogeny class.