Properties

Label 1.23.g
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

Learn more about

Invariants

Base field:  $\F_{23}$
Dimension:  $1$
L-polynomial:  $1 + 6 x + 23 x^{2}$
Frobenius angles:  $\pm0.715122617226$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-14}) \)
Galois group:  $C_2$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $30$ $540$ $11970$ $280800$ $6435150$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $30$ $540$ $11970$ $280800$ $6435150$ $148021020$ $3404942130$ $78310627200$ $1801152126270$ $41426522660700$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-14}) \).
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.ag$2$(not in LMFDB)