# Properties

 Label 1.277.am Base Field $\F_{277}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

# Learn more about

## Invariants

 Base field: $\F_{277}$ Dimension: $1$ L-polynomial: $1 - 12 x + 277 x^{2}$ Frobenius angles: $\pm0.382604351249$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-241})$$ 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 $A(\F_{q^r})$ 266 77140 21262178 5887324800 1630790565866 451729642512820 125129118403027298 34660765705114483200 9601032097149150437066 2659485890897933103783700

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 266 77140 21262178 5887324800 1630790565866 451729642512820 125129118403027298 34660765705114483200 9601032097149150437066 2659485890897933103783700

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{277}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-241})$$.
All geometric endomorphisms are defined over $\F_{277}$.

## 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 1.277.m $2$ (not in LMFDB)