Properties

Label 2.25.ao_du
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:  $( 1 - 8 x + 25 x^{2} )( 1 - 6 x + 25 x^{2} )$
Frobenius angles:  $\pm0.204832764699$, $\pm0.295167235301$
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
$A(\F_{q^r})$ 360 391680 249224040 153413222400 95432942413800 59604644711139840 37252166675977814760 23282963759721716121600 14551909127240506291918440 9094947017729100370214054400

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 626 15948 392734 9772332 244140626 6103394988 152587231294 3814695666252 95367431640626

Decomposition

1.25.ai $\times$ 1.25.ag

Base change

This is a primitive isogeny class.