# Properties

 Label 3.11.an_df_amz 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: $1 - 13 x + 83 x^{2} - 337 x^{3} + 913 x^{4} - 1573 x^{5} + 1331 x^{6}$ Frobenius angles: $\pm0.0419333658373$, $\pm0.241588088023$, $\pm0.421886769942$ Angle rank: $3$ (numerical) Number field: 6.0.403627375.1 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 $A(\F_{q^r})$ 405 1721655 2409010875 3116197271655 4157729688909375 5556186788680110375 7399646802705714626880 9848266864767932173362855 13108896537245525348720479125 17449123886179266530194197159375

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ -1 119 1361 14539 160299 1770371 19485584 214326979 2357750261 25937010799

## Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
 The endomorphism algebra of this simple isogeny class is 6.0.403627375.1.
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.n_df_mz $2$ (not in LMFDB)