# Properties

 Label 1.2.b Base field $\F_{2}$ Dimension $1$ $p$-rank $1$ Ordinary yes Supersingular no Simple yes Geometrically simple yes Primitive yes Principally polarizable yes Contains a Jacobian yes

# Related objects

## Invariants

 Base field: $\F_{2}$ Dimension: $1$ L-polynomial: $1 + x + 2 x^{2}$ Frobenius angles: $\pm0.615026728081$ Angle rank: $1$ (numerical) Number field: $$\Q(\sqrt{-7})$$ Galois group: $C_2$ Jacobians: 1

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

## Newton polygon

This isogeny class is ordinary. $p$-rank: $1$ Slopes: $[0, 1]$

## Point counts

This isogeny class contains the Jacobian of 1 curve (which is hyperelliptic), and hence is principally polarizable:

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $4$ $8$ $4$ $16$ $44$

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $4$ $8$ $4$ $16$ $44$ $56$ $116$ $288$ $508$ $968$

## Decomposition and endomorphism algebra

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

## Base change

This is a primitive isogeny class.

## Twists

Below is a list of all twists of this isogeny class.
TwistExtension degreeCommon base change
1.2.ab$2$1.4.d