# Properties

 Label 1.433.abh Base Field $\F_{433}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{433}$ Dimension: $1$ L-polynomial: $1 - 33 x + 433 x^{2}$ Frobenius angles: $\pm0.208549680842$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-643})$$ Galois group: $C_2$ Jacobians: 3

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 3 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 401 187267 81189668 35152450371 15220877909921 6590636901151744 2853745729114290929 1235671900486956602883 535045932924861225044324 231674888957022265054825507

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 401 187267 81189668 35152450371 15220877909921 6590636901151744 2853745729114290929 1235671900486956602883 535045932924861225044324 231674888957022265054825507

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{433}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-643})$$.
All geometric endomorphisms are defined over $\F_{433}$.

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.433.bh $2$ (not in LMFDB)