Properties

Label 3.11.ao_dq_aow
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:  $( 1 - 6 x + 11 x^{2} )( 1 - 8 x + 35 x^{2} - 88 x^{3} + 121 x^{4} )$
Frobenius angles:  $\pm0.140218899004$, $\pm0.167863583547$, $\pm0.388927483238$
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
$A(\F_{q^r})$ 366 1666764 2443414536 3166491578976 4187241531619806 5571444015329860800 7408617037465455461274 9852882714726166846710144 13110342536472274829531393496 17449148773472555112920303024844

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -2 114 1378 14770 161438 1775232 19509194 214427426 2358010342 25937047794

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.ag $\times$ 2.11.ai_bj 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_ac_bi$2$(not in LMFDB)
3.11.c_ac_abi$2$(not in LMFDB)
3.11.o_dq_ow$2$(not in LMFDB)