Properties

Label 3.11.an_dd_amk
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:  $( 1 - x + 11 x^{2} )( 1 - 6 x + 11 x^{2} )^{2}$
Frobenius angles:  $\pm0.140218899004$, $\pm0.140218899004$, $\pm0.451829325548$
Angle rank:  $2$ (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
$A(\F_{q^r})$ 396 1667952 2355076944 3115894459392 4187575203146676 5579766049572000000 7409873167779616546716 9851755237142869229617152 13110200328368082527594077104 17449545804474034197334210288752

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -1 115 1328 14535 161449 1777876 19512499 214402895 2357984768 25937637955

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.ag 2 $\times$ 1.11.ab 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.al_cf_ahy$2$(not in LMFDB)
3.11.ab_ad_o$2$(not in LMFDB)
3.11.b_ad_ao$2$(not in LMFDB)
3.11.l_cf_hy$2$(not in LMFDB)
3.11.n_dd_mk$2$(not in LMFDB)
3.11.f_be_ed$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.al_cf_ahy$2$(not in LMFDB)
3.11.ab_ad_o$2$(not in LMFDB)
3.11.b_ad_ao$2$(not in LMFDB)
3.11.l_cf_hy$2$(not in LMFDB)
3.11.n_dd_mk$2$(not in LMFDB)
3.11.f_be_ed$3$(not in LMFDB)
3.11.ab_z_ao$4$(not in LMFDB)
3.11.b_z_o$4$(not in LMFDB)
3.11.ah_bq_agb$6$(not in LMFDB)
3.11.af_be_aed$6$(not in LMFDB)
3.11.h_bq_gb$6$(not in LMFDB)
3.11.af_x_ads$8$(not in LMFDB)
3.11.ad_p_adc$8$(not in LMFDB)
3.11.d_p_dc$8$(not in LMFDB)
3.11.f_x_ds$8$(not in LMFDB)