# Properties

 Label 3.11.an_da_als Base Field $\F_{11}$ Dimension $3$ Ordinary Yes $p$-rank $3$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{11}$ Dimension: $3$ L-polynomial: $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 25 x^{2} - 77 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.0530380253560$, $\pm0.140218899004$, $\pm0.477974681599$ Angle rank: $3$ (numerical)

This isogeny class is not simple.

## Newton polygon

This isogeny class is ordinary.

 $p$-rank: $3$ Slopes: $[0, 0, 0, 1, 1, 1]$

## 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 $A(\F_{q^r})$ 378 1571724 2244302802 3058612625376 4168520769496608 5570391311448648300 7403839930515044019402 9849519412573842587988864 13110008037839783389644043698 17449655321335045828037617234944

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 109 1265 14265 160714 1774897 19496623 214354241 2357950181 25937800744

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.ah_z 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 3.11.ab_ag_ae $2$ (not in LMFDB) 3.11.b_ag_e $2$ (not in LMFDB) 3.11.n_da_ls $2$ (not in LMFDB)