Properties

Label 2.41.at_go
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:  $( 1 - 11 x + 41 x^{2} )( 1 - 8 x + 41 x^{2} )$
Frobenius angles:  $\pm0.171113726078$, $\pm0.285223287477$
Angle rank:  $2$ (numerical)
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1054 2793100 4784299936 7998723366400 13425475059245854 22563739279662880000 37929195072096531135454 63759020409046519698585600 107178931957461386093389910176 180167783822433442599517794527500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 23 1661 69416 2830641 115880503 4750156658 194754108943 7984923913441 327381937417736 13422659374671101

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The isogeny class factors as 1.41.al $\times$ 1.41.ai 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.41.ad_ag$2$(not in LMFDB)
2.41.d_ag$2$(not in LMFDB)
2.41.t_go$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.41.ad_ag$2$(not in LMFDB)
2.41.d_ag$2$(not in LMFDB)
2.41.t_go$2$(not in LMFDB)
2.41.av_hk$4$(not in LMFDB)
2.41.ab_abc$4$(not in LMFDB)
2.41.b_abc$4$(not in LMFDB)
2.41.v_hk$4$(not in LMFDB)