Properties

Label 2.41.as_ge
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:  $1 - 18 x + 160 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.183705984994$, $\pm0.307898514763$
Angle rank:  $2$ (numerical)
Number field:  4.0.781632.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1086 2821428 4791224574 7998421094352 13424763666724206 22563530631755478612 37929182432164588426254 63759030003971981067138048 107178934391474931616704695694 180167783259825574516798829600148

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1678 69516 2830534 115874364 4750112734 194754044040 7984925115070 327381944852520 13422659332756318

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.781632.1.
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.s_ge$2$(not in LMFDB)