Properties

Label 2.41.as_gb
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:  $1 - 18 x + 157 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.147848350106$, $\pm0.329086721394$
Angle rank:  $2$ (numerical)
Number field:  4.0.2295360.4
Galois group:  $D_{4}$
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1083 2810385 4779967788 7992805199625 13423262086230483 22563451626257373840 37929298599953540648643 63759087075421802837039625 107178948739642122094446884268 180167785066056966675074312504625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1672 69354 2828548 115861404 4750096102 194754640524 7984932262468 327381988679514 13422659467322152

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.2295360.4.
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_gb$2$(not in LMFDB)