Properties

Label 2.25.an_dm
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:  $( 1 - 8 x + 25 x^{2} )( 1 - 5 x + 25 x^{2} )$
Frobenius angles:  $\pm0.204832764699$, $\pm0.333333333333$
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
$A(\F_{q^r})$ 378 398412 249475464 153245191680 95397773496858 59602753904101632 37252622983320422874 23283073667168587560960 14551916993505378064915848 9094946107833483029052959052

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 637 15964 392305 9768733 244132882 6103469749 152587951585 3814697728348 95367422099677

Decomposition

1.25.ai $\times$ 1.25.af

Base change

This is a primitive isogeny class.