Properties

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

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-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:  $D_{4}$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, 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 and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.22725.1.
All geometric endomorphisms are defined over $\F_{23}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.23.p_dx$2$(not in LMFDB)