# Properties

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

## Invariants

 Base field: $\F_{277}$ Dimension: $1$ L-polynomial: $1 - 26 x + 277 x^{2}$ Frobenius angles: $\pm0.214661789861$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ Galois group: $C_2$ Jacobians: 14

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 14 curves, and hence is principally polarizable:

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 252 76608 21257964 5887478016 1630795511772 451729694235456 125129118021420492 34660765686126117888 9601032096923002094268 2659485890897797971739968

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 252 76608 21257964 5887478016 1630795511772 451729694235456 125129118021420492 34660765686126117888 9601032096923002094268 2659485890897797971739968

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{277}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{277}$.

## 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 1.277.ba $2$ (not in LMFDB) 1.277.af $3$ (not in LMFDB) 1.277.bf $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.277.ba $2$ (not in LMFDB) 1.277.af $3$ (not in LMFDB) 1.277.bf $3$ (not in LMFDB) 1.277.abf $6$ (not in LMFDB) 1.277.f $6$ (not in LMFDB)