Properties

Label 2.25.an_dj
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:  $1 - 13 x + 87 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.158125293436$, $\pm0.36172442682$
Angle rank:  $2$ (numerical)
Number field:  4.0.824229.1
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
$A(\F_{q^r})$ 375 394125 247620375 152867293125 95365394430000 59605612452091125 37253899343139003375 23283257230002377113125 14551929144571932292188375 9094945876744018903982880000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 631 15847 391339 9765418 244144591 6103678867 152589154579 3814700913673 95367419676526

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.