# Properties

 Label 1.443.a Base Field $\F_{443}$ Dimension $1$ Ordinary No $p$-rank $0$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{443}$ Dimension: $1$ L-polynomial: $1 + 443 x^{2}$ Frobenius angles: $\pm0.5$ Angle rank: $0$ (numerical) Number field: $$\Q(\sqrt{-443})$$ Galois group: $C_2$ Jacobians: 20

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 20 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 444 197136 86938308 38513277504 17061555810444 7558269397902864 3348313266243628308 1483302776868900000000 657103130187045811620444 291096686672895417659477136

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 444 197136 86938308 38513277504 17061555810444 7558269397902864 3348313266243628308 1483302776868900000000 657103130187045811620444 291096686672895417659477136

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{443}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-443})$$.
Endomorphism algebra over $\overline{\F}_{443}$
 The base change of $A$ to $\F_{443^{2}}$ is the simple isogeny class 1.196249.bic and its endomorphism algebra is the quaternion algebra over $$\Q$$ ramified at $443$ and $\infty$.
All geometric endomorphisms are defined over $\F_{443^{2}}$.

## Base change

This is a primitive isogeny class.

## Twists

This isogeny class has no twists.