# Properties

 Label 1.443.abq Base Field $\F_{443}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{443}$ Dimension: $1$ L-polynomial: $1 - 42 x + 443 x^{2}$ Frobenius angles: $\pm0.0214037853635$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-2})$$ Galois group: $C_2$ Jacobians: 1

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 1 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 402 195372 86920038 38513291616 17061548011842 7558269064109964 3348313262981924982 1483302776879778715008 657103130185712503944114 291096686672834599466322732

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 402 195372 86920038 38513291616 17061548011842 7558269064109964 3348313262981924982 1483302776879778715008 657103130185712503944114 291096686672834599466322732

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{443}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-2})$$.
All geometric endomorphisms are defined over $\F_{443}$.

## 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 1.443.bq $2$ (not in LMFDB)