Properties

Label 2.41.as_fu
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:  $1 - 18 x + 150 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0564278675068$, $\pm0.361596525321$
Angle rank:  $2$ (numerical)
Number field:  4.0.116272.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1076 2784688 4753734644 7979311827712 13419029081485556 22562608280459359792 37929188321937816103604 63759066645192640858533888 107178939521105083174709430644 180167782472032291684741320352048

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1658 68976 2823774 115824864 4749918554 194754074280 7984929703870 327381960521160 13422659274065018

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.116272.1.
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_fu$2$(not in LMFDB)