# Properties

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

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $1 - 6 x + 19 x^{2} - 66 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.0720381525652$, $\pm0.522289064218$ Angle rank: $2$ (numerical) Number field: 4.0.13968.2 Galois group: $D_{4}$ Jacobians: 6

This isogeny class is simple and geometrically 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:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 69 14697 1679184 208829673 25927023309 3141739830528 379671182865141 45945902956345353 5560155171605311056 672761716727880170457

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 124 1260 14260 160986 1773430 19483134 214341028 2358048564 25937876524

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.13968.2.
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.g_t $2$ 2.121.c_ahh