Properties

Label 2.25.an_dh
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:  $1 - 13 x + 85 x^{2} - 325 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.128789547124$, $\pm0.375668685983$
Angle rank:  $2$ (numerical)
Number field:  4.0.44573.1
Galois group:  $D_4$

This isogeny class is simple.

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
$A(\F_{q^r})$ 373 391277 246386269 152607811925 95337474393808 59605084445673677 37254189279234038869 23283302227780352730725 14551933747616889577120333 9094946824598428283699146752

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 13 627 15769 390675 9762558 244142427 6103726369 152589449475 3814702120333 95367429615502

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.