Properties

Label 2.41.av_hi
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:  $( 1 - 12 x + 41 x^{2} )( 1 - 9 x + 41 x^{2} )$
Frobenius angles:  $\pm0.113551764296$, $\pm0.251940962052$
Angle rank:  $2$ (numerical)
Jacobians:  6

This isogeny class is not 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
$A(\F_{q^r})$ 990 2726460 4758831000 7993064629440 13424895517794750 22563819472715136000 37929237987933420172110 63759029113231317298287360 107178934881384557380968471000 180167785978512555597338603941500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 21 1621 69048 2828641 115875501 4750173538 194754329301 7984925003521 327381946348968 13422659535300901

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The isogeny class factors as 1.41.am $\times$ 1.41.aj and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ad_aba$2$(not in LMFDB)
2.41.d_aba$2$(not in LMFDB)
2.41.v_hi$2$(not in LMFDB)