Properties

Label 2.25.at_fk
Base Field $\F_{5^2}$
Dimension $2$
$p$-rank $1$
Principally polarizable
Does not contain a Jacobian

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 5 x )^{2}( 1 - 9 x + 25 x^{2} )$
Frobenius angles:  $0.0$, $0.0$, $\pm0.143566293129$
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
$A(\F_{q^r})$ 272 342720 239435072 152212919040 95344975303952 59603932464168960 37252902856448281232 23283051620853824916480 14551909382478978129326912 9094945529005546284671889600

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 7 545 15322 389665 9763327 244137710 6103515607 152587807105 3814695733162 95367416030225

Decomposition

1.25.ak $\times$ 1.25.aj

Base change

This is a primitive isogeny class.