Properties

Label 2.23.ap_dx
Base Field $\F_{23}$
Dimension $2$
$p$-rank $2$
Principally polarizable
Contains a Jacobian

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
Weil polynomial:  $1 - 15 x + 101 x^{2} - 345 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.144663500024$, $\pm0.268275520367$
Angle rank:  $2$ (numerical)
Number field:  4.0.22725.1
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
$A(\F_{q^r})$ 271 268561 149694709 78672527901 41463219189136 21916704893434441 11592864868189732489 6132609714002320372725 3244152443966475138358411 1716156209946980857250288896

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 9 507 12303 281131 6442044 148049943 3404833833 78310976323 1801153513179 41426520353022

Decomposition

This is a simple isogeny class.

Base change

This is a primitive isogeny class.