Properties

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

Learn more about

Invariants

Base field:  $\F_{5^2}$
Dimension:  $2$
Weil polynomial:  $1 - 17 x + 121 x^{2} - 425 x^{3} + 625 x^{4}$
Frobenius angles:  $\pm0.0882611637788$, $\pm0.235677669977$
Angle rank:  $2$ (numerical)
Number field:  4.0.8525.1
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
$A(\F_{q^r})$ 305 362645 243880745 152850878405 95407952922000 59607387719481605 37252815730859812745 23283024697531434104645 14551913290584695922143105 9094947945039117554393088000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 579 15609 391299 9769774 244151859 6103501329 152587630659 3814696757649 95367441364174

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.