# Properties

 Label 1.269.n Base Field $\F_{269}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{269}$ Dimension: $1$ L-polynomial: $1 + 13 x + 269 x^{2}$ Frobenius angles: $\pm0.629710138635$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-907})$$ Galois group: $C_2$ Jacobians: 3

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 3 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 283 72731 19456816 5236122883 1408516872143 378890438521664 101921535812684507 27416893192980228963 7375144266028150255984 1983913807583088308159651

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 283 72731 19456816 5236122883 1408516872143 378890438521664 101921535812684507 27416893192980228963 7375144266028150255984 1983913807583088308159651

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{269}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-907})$$.
All geometric endomorphisms are defined over $\F_{269}$.

## 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 1.269.an $2$ (not in LMFDB)