# Properties

 Label 1.23.a Base field $\F_{23}$ Dimension $1$ $p$-rank $0$ Ordinary no Supersingular yes Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

## Invariants

 Base field: $\F_{23}$ Dimension: $1$ L-polynomial: $1 + 23 x^{2}$ Frobenius angles: $\pm0.5$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-23})$$ Galois group: $C_2$ Jacobians: 6

This isogeny class is simple and geometrically simple.

## Newton polygon

This isogeny class is supersingular. $p$-rank: $0$ Slopes: $[1/2, 1/2]$

## Point counts

This isogeny class contains the Jacobians of 6 curves, and hence is principally polarizable:

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $24$ $576$ $12168$ $278784$ $6436344$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $24$ $576$ $12168$ $278784$ $6436344$ $148060224$ $3404825448$ $78310425600$ $1801152661464$ $41426524086336$

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{23}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-23})$$.
Endomorphism algebra over $\overline{\F}_{23}$
 The base change of $A$ to $\F_{23^{2}}$ is the simple isogeny class 1.529.bu and its endomorphism algebra is the quaternion algebra over $$\Q$$ ramified at $23$ and $\infty$.
All geometric endomorphisms are defined over $\F_{23^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

This isogeny class has no twists.