Properties

Label 3.11.ap_ee_arn
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:  $( 1 - 5 x + 11 x^{2} )^{3}$
Frobenius angles:  $\pm0.228229222880$, $\pm0.228229222880$, $\pm0.228229222880$
Angle rank:  $1$ (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
$A(\F_{q^r})$ 343 1685159 2582630848 3291326171875 4233994921204433 5569931768213786624 7397215398464534471843 9846286021072917404296875 13108397687134511225731882048 17448991513836070999556906276039

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -3 113 1452 15341 163227 1774748 19479177 214283861 2357660532 25936814033

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{11}$
The isogeny class factors as 1.11.af 3 and its endomorphism algebra is $\mathrm{M}_{3}($\(\Q(\sqrt{-19}) \)$)$
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.af_i_p$2$(not in LMFDB)
3.11.f_i_ap$2$(not in LMFDB)
3.11.p_ee_rn$2$(not in LMFDB)
3.11.a_a_bo$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
3.11.af_i_p$2$(not in LMFDB)
3.11.f_i_ap$2$(not in LMFDB)
3.11.p_ee_rn$2$(not in LMFDB)
3.11.a_a_bo$3$(not in LMFDB)
3.11.af_o_ap$4$(not in LMFDB)
3.11.f_o_p$4$(not in LMFDB)
3.11.ak_by_agy$6$(not in LMFDB)
3.11.a_a_abo$6$(not in LMFDB)
3.11.k_by_gy$6$(not in LMFDB)