# Properties

 Label 3.11.an_dc_ame 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: $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 27 x^{2} - 77 x^{3} + 121 x^{4} )$ Frobenius angles: $\pm0.116678659763$, $\pm0.140218899004$, $\pm0.461158112795$ 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 $A(\F_{q^r})$ 390 1635660 2317941990 3097612908000 4183049482716000 5578410303754879500 7408941997991615729310 9851543525232829029168000 13110413880450992321633581710 17449729852153104431626656384000

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 113 1307 14449 161274 1777445 19510049 214398289 2358023177 25937911528

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The isogeny class factors as 1.11.ag $\times$ 2.11.ah_bb 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_ae_i $2$ (not in LMFDB) 3.11.b_ae_ai $2$ (not in LMFDB) 3.11.n_dc_me $2$ (not in LMFDB)