Properties

Label 2.41.av_hh
Base Field $\F_{41}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{41}$
Dimension:  $2$
L-polynomial:  $1 - 21 x + 189 x^{2} - 861 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0895520221991$, $\pm0.262353290689$
Angle rank:  $2$ (numerical)
Number field:  4.0.188773.1
Galois group:  $D_{4}$
Jacobians:  3

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class contains the Jacobians of 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 989 2722717 4754440469 7990218721333 13423642423672784 22563415794468383293 37929144199923688788701 63759016316936981557022373 107178935676419235326651791301 180167787077539419765035434258432

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 21 1619 68985 2827635 115864686 4750088555 194753847729 7984923400963 327381948777429 13422659617179374

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.188773.1.
All geometric endomorphisms are defined over $\F_{41}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.41.v_hh$2$(not in LMFDB)