Properties

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

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Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $( 1 - 9 x + 25 x^{2} )( 1 - 3 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.403013315979$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 391 396865 246411328 152533078425 95345043690991 59609620624261120 37254663539943167023 23283261695514368190825 14551918489662379664420416 9094945537345523891958439825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 14 636 15770 390484 9763334 244161006 6103804070 152589183844 3814698120554 95367416117676

Decomposition

1.25.aj $\times$ 1.25.ad

Base change

This is a primitive isogeny class.