# Properties

 Label 1.353.abi 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: $1 - 34 x + 353 x^{2}$ Frobenius angles: $\pm0.140006242475$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-1})$$ Galois group: $C_2$ Jacobians: 8

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 8 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 320 124160 43983680 15527449600 5481175969600 1934854222695680 683003515045913920 241100240257759334400 85108384801196481807680 30043259834684778170604800

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 320 124160 43983680 15527449600 5481175969600 1934854222695680 683003515045913920 241100240257759334400 85108384801196481807680 30043259834684778170604800

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{353}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-1})$$.
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.bi $2$ (not in LMFDB) 1.353.aq $4$ (not in LMFDB) 1.353.q $4$ (not in LMFDB)