# Properties

 Label 3.11.ao_do_aol 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: $1 - 14 x + 92 x^{2} - 375 x^{3} + 1012 x^{4} - 1694 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0370510590969$, $\pm0.180631153359$, $\pm0.411625911318$ Angle rank: $3$ (numerical) Number field: 6.0.31633587.1 Galois group: $S_4\times C_2$

This isogeny class is simple and geometrically 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 $A(\F_{q^r})$ 353 1595207 2349243593 3102660067723 4159230790999603 5560792831378351367 7403333932962076457113 9849975362083673459044947 13109193017918985425051840192 17448936333570654521812839442367

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -2 110 1327 14474 160358 1771841 19495292 214364162 2357803588 25936732010

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.31633587.1.
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.o_do_ol $2$ (not in LMFDB)