Properties

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

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x )^{2}( 1 - 2 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.435905783151$
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
$A(\F_{q^r})$ 384 387072 242448768 151763189760 95254866985344 59599722065651712 37252890594799294848 23282949931463587921920 14551885858226333584097664 9094944357023688680860772352

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 622 15518 388510 9754094 244120462 6103513598 152587140670 3814689566414 95367403741102

Decomposition

1.25.ak $\times$ 1.25.ac

Base change

This is a primitive isogeny class.