Properties

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

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Invariants

Base field:  $\F_{11}$
Dimension:  $3$
L-polynomial:  $1 - 13 x + 83 x^{2} - 335 x^{3} + 913 x^{4} - 1573 x^{5} + 1331 x^{6}$
Frobenius angles:  $\pm0.103580074935$, $\pm0.211515765637$, $\pm0.427737152978$
Angle rank:  $3$ (numerical)
Number field:  6.0.409598903.1
Galois group:  $A_4\times C_2$

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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 407 1729343 2423008973 3138759274343 4180009221724897 5570317596937297127 7405986445700293972928 9850451069210305306846247 13109525713904930607621113867 17449275426000273468101886632543

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 119 1367 14643 161159 1774871 19502272 214374515 2357863433 25937236059

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The endomorphism algebra of this simple isogeny class is 6.0.409598903.1.
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.
TwistExtension DegreeCommon base change
3.11.n_df_mx$2$(not in LMFDB)