Properties

Label 3.11.ao_dr_apc
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 36 x^{2} - 88 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.140218899004$, $\pm0.196063835166$, $\pm0.372536541753$
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
$A(\F_{q^r})$ 372 1700784 2487136572 3191106184704 4191399146410932 5568186683287825200 7406020776080204590908 9852036735821877591146496 13110203349394585193168206452 17449111854549923398582228930224

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 116 1402 14884 161598 1774196 19502362 214409020 2357985310 25936992916

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.ag $\times$ 2.11.ai_bk 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.ac_ab_bo$2$(not in LMFDB)
3.11.c_ab_abo$2$(not in LMFDB)
3.11.o_dr_pc$2$(not in LMFDB)