# Properties

 Label 1.353.j Base Field $\F_{353}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{353}$ Dimension: $1$ L-polynomial: $1 + 9 x + 353 x^{2}$ Frobenius angles: $\pm0.576987061859$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-11})$$ Galois group: $C_2$ Jacobians: 12

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 12 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 363 125235 43978176 15527261475 5481177596763 1934854156097280 683003511755733531 241100240239945966275 85108384801276729725888 30043259834673172633902675

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 363 125235 43978176 15527261475 5481177596763 1934854156097280 683003511755733531 241100240239945966275 85108384801276729725888 30043259834673172633902675

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{353}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-11})$$.
All geometric endomorphisms are defined over $\F_{353}$.

## 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 1.353.aj $2$ (not in LMFDB)