Properties

Label 2.41.as_fv
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:  $1 - 18 x + 151 x^{2} - 738 x^{3} + 1681 x^{4}$
Frobenius angles:  $\pm0.0737449254048$, $\pm0.357708845091$
Angle rank:  $2$ (numerical)
Number field:  4.0.166032.2
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1077 2788353 4757479488 7981272881433 13419696318179757 22562785758466003968 37929238087133082166413 63759084431578340749669737 107178945938393199920974352448 180167784321373025185937304447633

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1660 69030 2824468 115830624 4749955918 194754329808 7984931931364 327381980122998 13422659411842540

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The endomorphism algebra of this simple isogeny class is 4.0.166032.2.
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_fv$2$(not in LMFDB)