# Properties

 Label 2.11.ah_bi 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 No

## Invariants

 Base field: $\F_{11}$ Dimension: $2$ L-polynomial: $( 1 - 4 x + 11 x^{2} )( 1 - 3 x + 11 x^{2} )$ Frobenius angles: $\pm0.293962833700$, $\pm0.350615407277$ Angle rank: $2$ (numerical) Jacobians: 0

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 is principally polarizable, but does not contain a Jacobian.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 72 17280 1965600 218488320 25857660312 3130493184000 379556044625592 45952044838778880 5560220695437626400 672758038151896752000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 5 141 1472 14921 160555 1767078 19477225 214369681 2358076352 25937734701

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ae $\times$ 1.11.ad 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.ab_k $2$ 2.121.t_mi 2.11.b_k $2$ 2.121.t_mi 2.11.h_bi $2$ 2.121.t_mi