Properties

Label 2.41.aw_ht
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:  $1 - 22 x + 201 x^{2} - 902 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0789642873101$, $\pm0.230762790725$
Angle rank:  $2$ (numerical)
Number field:  4.0.45632.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 959 2691913 4744061756 7988954416793 13424058719930719 22563668704226881168 37929194619491139697439 63759009104968249758154217 107178926745281611659133934204 180167783644507226540139088943833

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 20 1600 68834 2827188 115868280 4750141798 194754106616 7984922497764 327381921496946 13422659361415440

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.45632.1.
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.w_ht$2$(not in LMFDB)