Properties

Label 2.25.aq_ej
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:  $( 1 - 9 x + 25 x^{2} )( 1 - 7 x + 25 x^{2} )$
Frobenius angles:  $\pm0.143566293129$, $\pm0.253183311107$
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
$A(\F_{q^r})$ 323 373065 246162176 153189815625 95446998996563 59611105171537920 37253136669806107331 23283052002172707215625 14551914736669321619548928 9094947577617366807042294825

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 10 596 15754 392164 9773770 244167086 6103553914 152587809604 3814697136730 95367437511476

Decomposition

1.25.aj $\times$ 1.25.ah

Base change

This is a primitive isogeny class.