Properties

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

Learn more about

Invariants

Base field:  $\F_{41}$
Dimension:  $2$
L-polynomial:  $1 - 20 x + 177 x^{2} - 820 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0953421678685$, $\pm0.292668588087$
Angle rank:  $2$ (numerical)
Number field:  4.0.37025.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1019 2750281 4761110384 7989635062025 13422763808553979 22563165608669092096 37929143594698973338859 63759042502908302154118025 107178946498374746323041553904 180167789061443155593076886768041

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 22 1636 69082 2827428 115857102 4750035886 194753844622 7984926680388 327381981833482 13422659764981956

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.37025.1.
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.u_gv$2$(not in LMFDB)