# Properties

 Label 2.11.ag_v 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: $1 - 6 x + 21 x^{2} - 66 x^{3} + 121 x^{4}$ Frobenius angles: $\pm0.120671085495$, $\pm0.507787998454$ Angle rank: $2$ (numerical) Number field: 4.0.424000.2 Galois group: $D_{4}$ Jacobians: 2

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 2 curves, and hence is principally polarizable:

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

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 71 15265 1726436 210672265 25994784191 3146153380240 379872513083351 45949812198728265 5560188022020297476 672764754652325040625

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 6 128 1296 14388 161406 1775918 19493466 214359268 2358062496 25937993648

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 4.0.424000.2.
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_v $2$ 2.121.g_aef