Properties

Label 2.25.ao_dr
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 25 x^{2} )( 1 - 5 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.333333333333$
Angle rank:  $1$ (numerical)

Newton polygon

$p$-rank:  $1$
Slopes:  $[0, 1/2, 1/2, 1]$

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
$A(\F_{q^r})$ 357 387345 247221072 152945884665 95375505232077 59603932464168960 37253379705812109357 23283230435605803432105 14551939184819911035576912 9094948322973384999759780225

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 620 15822 391540 9766452 244137710 6103593732 152588978980 3814703545662 95367445327100

Decomposition

1.25.aj $\times$ 1.25.af

Base change

This is a primitive isogeny class.