Properties

Label 1.23.ae
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:  $1 - 4 x + 23 x^{2}$
Frobenius angles:  $\pm0.363071407864$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-19}) \)
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $20$ $560$ $12380$ $280000$ $6432100$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $20$ $560$ $12380$ $280000$ $6432100$ $148015280$ $3404840620$ $78311520000$ $1801154451380$ $41426506074800$

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-19}) \).
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.e$2$(not in LMFDB)