# Properties

 Label 1.49.al Base Field $\F_{7^{2}}$ Dimension $1$ Ordinary Yes $p$-rank $1$ Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{7^{2}}$ Dimension: $1$ L-polynomial: $1 - 11 x + 49 x^{2}$ Frobenius angles: $\pm0.212295615010$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-3})$$ 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 $A(\F_{q^r})$ 39 2379 117936 5769075 282508239 13841440704 678223144911 33232923840675 1628413520361264 79792265774288379

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 39 2379 117936 5769075 282508239 13841440704 678223144911 33232923840675 1628413520361264 79792265774288379

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{7^{2}}$
 The endomorphism algebra of this simple isogeny class is $$\Q(\sqrt{-3})$$.
All geometric endomorphisms are defined over $\F_{7^{2}}$.

## Base change

This isogeny class is not primitive. It is a base change from the following isogeny classes over subfields of $\F_{7^{2}}$.

 Subfield Primitive Model $\F_{7}$ 1.7.af $\F_{7}$ 1.7.f

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 1.49.l $2$ (not in LMFDB) 1.49.ac $3$ (not in LMFDB) 1.49.n $3$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 1.49.l $2$ (not in LMFDB) 1.49.ac $3$ (not in LMFDB) 1.49.n $3$ (not in LMFDB) 1.49.an $6$ (not in LMFDB) 1.49.c $6$ (not in LMFDB)