Properties

Label 2.41.as_fy
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:  $( 1 - 12 x + 41 x^{2} )( 1 - 6 x + 41 x^{2} )$
Frobenius angles:  $\pm0.113551764296$, $\pm0.344786929280$
Angle rank:  $2$ (numerical)
Jacobians:  46

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 46 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 1080 2799360 4768719480 7987089162240 13421572979067000 22563203849571168000 37929318476855600472120 63759106916838493051944960 107178954017719783117741454520 180167786296072881445675492704000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 24 1666 69192 2826526 115846824 4750043938 194754742584 7984934747326 327382004801592 13422659558959426

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{41}$
The isogeny class factors as 1.41.am $\times$ 1.41.ag 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.ag_k$2$(not in LMFDB)
2.41.g_k$2$(not in LMFDB)
2.41.s_fy$2$(not in LMFDB)