# Properties

 Label 1.463.a Base Field $\F_{463}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{463}$ Dimension: $1$ L-polynomial: $1 + 463 x^{2}$ Frobenius angles: $\pm0.5$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-463})$$ Galois group: $C_2$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 464 215296 99252848 45953639424 21276733558544 9851127836111104 4561072096211304368 2111776380453925785600 977752464192721105849424 452699390921272425475399936

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 464 215296 99252848 45953639424 21276733558544 9851127836111104 4561072096211304368 2111776380453925785600 977752464192721105849424 452699390921272425475399936

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{463}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-463})$$.
Endomorphism algebra over $\overline{\F}_{463}$
 The base change of $A$ to $\F_{463^{2}}$ is the simple isogeny class 1.214369.bjq and its endomorphism algebra is the quaternion algebra over $$\Q$$ ramified at $463$ and $\infty$.
All geometric endomorphisms are defined over $\F_{463^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

This isogeny class has no twists.