Properties

Label 2.25.aq_eg
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:  $( 1 - 5 x )^{2}( 1 - 6 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.295167235301$
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
$A(\F_{q^r})$ 320 368640 243863360 152510791680 95311041953600 59591277834117120 37251016204308050240 23282894853620587560960 14551907362095304816297280 9094946996302322961200947200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 590 15610 390430 9759850 244085870 6103206490 152586779710 3814695203530 95367431415950

Decomposition

1.25.ak $\times$ 1.25.ag

Base change

This is a primitive isogeny class.