Properties

Label 1.23.c
Base field $\F_{23}$
Dimension $1$
$p$-rank $1$
Ordinary yes
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:  $1$
L-polynomial:  $1 + 2 x + 23 x^{2}$
Frobenius angles:  $\pm0.566862818396$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-22}) \)
Galois group:  $C_2$
Jacobians:  2

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $26$ $572$ $12038$ $279136$ $6440746$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $26$ $572$ $12038$ $279136$ $6440746$ $148043324$ $3404709334$ $78311046528$ $1801155209594$ $41426504708732$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-22}) \).
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
1.23.ac$2$(not in LMFDB)