# Properties

 Label 2.11.ag_bb 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: $( 1 - 5 x + 11 x^{2} )( 1 - x + 11 x^{2} )$ Frobenius angles: $\pm0.228229222880$, $\pm0.451829325548$ Angle rank: $2$ (numerical) Jacobians: 6

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 6 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 77 17017 1871408 214839625 25965370277 3143216876800 379847950463597 45942158108471625 5559467600654892848 672745195986494768137

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 140 1404 14676 161226 1774262 19492206 214323556 2357756964 25937239580

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.af $\times$ 1.11.ab 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.ae_r $2$ 2.121.s_gx 2.11.e_r $2$ 2.121.s_gx 2.11.g_bb $2$ 2.121.s_gx