# Properties

 Label 2.11.af_q Base field $\F_{11}$ Dimension $2$ $p$-rank $2$ Ordinary Yes Supersingular No Simple No Geometrically simple No Primitive Yes Principally polarizable Yes Contains a Jacobian Yes

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 + x + 11 x^{2} )$ Frobenius angles: $\pm0.140218899004$, $\pm0.548170674452$ Angle rank: $2$ (numerical) Jacobians: 4

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $2$ Slopes: $[0, 0, 1, 1]$

## Point counts

This isogeny class contains the Jacobians of 4 curves, and hence is principally polarizable:

• $y^2=10x^6+6x^3+5x^2+7x+4$
• $y^2=10x^6+3x^5+3x^4+5x^3+7x^2+8x+4$
• $y^2=7x^6+3x^5+3x^4+x^3+2x^2+6x+2$
• $y^2=7x^6+9x^5+6x^4+5x^3+5x^2+3x+8$

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 78 15444 1708200 212138784 26103086178 3145479480000 379771532895378 45953341316049024 5560297071958441800 672753001834059172884

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 7 129 1282 14489 162077 1775538 19488287 214375729 2358108742 25937540529

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 1.11.b and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{11}$.

## 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 2.11.ah_bc $2$ 2.121.h_aca 2.11.f_q $2$ 2.121.h_aca 2.11.h_bc $2$ 2.121.h_aca