Properties

Label 3.11.an_df_amw
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 7 x + 30 x^{2} - 77 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.140218899004$, $\pm0.183470593443$, $\pm0.430420419745$
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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 408 1733184 2430016992 3150068852736 4191170058284808 5577361391943244800 7409053685774983111032 9851355303391803069333504 13109616311355365973025035168 17449154643240059977423893985344

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 119 1370 14695 161589 1777112 19510343 214394191 2357879726 25937056519

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.ag $\times$ 2.11.ah_be 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.
TwistExtension DegreeCommon base change
3.11.ab_ab_ba$2$(not in LMFDB)
3.11.b_ab_aba$2$(not in LMFDB)
3.11.n_df_mw$2$(not in LMFDB)