Properties

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

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 7 x + 25 x^{2} )^{2}$
Frobenius angles:  $\pm0.253183311107$, $\pm0.253183311107$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

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

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
$A(\F_{q^r})$ 361 393129 249892864 153566015625 95449363292761 59603730228117504 37251463276849768489 23282826710353766015625 14551896134432380355547136 9094947389662651049822253129

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 628 15990 393124 9774012 244136878 6103279740 152586333124 3814692260262 95367435540628

Decomposition

1.25.ah 2

Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{5^2}$.

SubfieldPrimitive Model
$\F_{5}$2.5.a_ah