# Properties

 Label 1.241.ao Base Field $\F_{241}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{241}$ Dimension: $1$ L-polynomial: $1 - 14 x + 241 x^{2}$ Frobenius angles: $\pm0.351099664439$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 16

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 16 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 228 58368 14004900 3373436928 812988720228 195930567705600 47219273131464228 11379844844127141888 2742542606185086896100 660952768068426114352128

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 228 58368 14004900 3373436928 812988720228 195930567705600 47219273131464228 11379844844127141888 2742542606185086896100 660952768068426114352128

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{241}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{241}$.

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 1.241.o $2$ (not in LMFDB) 1.241.ar $3$ (not in LMFDB) 1.241.bf $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.241.o $2$ (not in LMFDB) 1.241.ar $3$ (not in LMFDB) 1.241.bf $3$ (not in LMFDB) 1.241.abf $6$ (not in LMFDB) 1.241.r $6$ (not in LMFDB)