# Properties

 Label 1.433.abi 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: $1 - 34 x + 433 x^{2}$ Frobenius angles: $\pm0.195653294268$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 18

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 18 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 400 187200 81187600 35152416000 15220877962000 6590636925537600 2853745730035200400 1235671900508133504000 535045932925147003219600 231674888957021456938056000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 400 187200 81187600 35152416000 15220877962000 6590636925537600 2853745730035200400 1235671900508133504000 535045932925147003219600 231674888957021456938056000

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{433}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
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.bi $2$ (not in LMFDB) 1.433.ay $4$ (not in LMFDB) 1.433.y $4$ (not in LMFDB)