Properties

Label 2.25.ao_dq
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:  $1 - 14 x + 94 x^{2} - 350 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.125226661552$, $\pm0.341943888296$
Angle rank:  $2$ (numerical)
Number field:  4.0.28400.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 356 385904 246554564 152787111680 95353633346436 59602533251174384 37253473021149890084 23283263955337086955520 14551943420168216498955236 9094948791807146374566373104

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 12 618 15780 391134 9764212 244131978 6103609020 152589198654 3814704655932 95367450243178

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.