Properties

Label 2.23.al_cr
Base field $\F_{23}$
Dimension $2$
$p$-rank $1$
Ordinary no
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{23}$
Dimension:  $2$
L-polynomial:  $1 - 11 x + 69 x^{2} - 253 x^{3} + 529 x^{4}$
Frobenius angles:  $\pm0.174086733330$, $\pm0.405448433343$
Angle rank:  $2$ (numerical)
Number field:  4.0.1760213.1
Galois group:  $D_{4}$
Jacobians:  $8$
Isomorphism classes:  8

This isogeny class is simple and geometrically simple, primitive, not ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

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

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $335$ $289105$ $150338285$ $78372028925$ $41423951738800$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $13$ $547$ $12355$ $280059$ $6435948$ $148054879$ $3405017629$ $78311574051$ $1801150891135$ $41426489691582$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{23}$.

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is 4.0.1760213.1.

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.l_cr$2$(not in LMFDB)