Properties

Label 2.61.ay_jx
Base Field $\F_{61}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{61}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 61 x^{2} )( 1 - 9 x + 61 x^{2} )$
Frobenius angles:  $\pm0.0900194921159$, $\pm0.304548188780$
Angle rank:  $2$ (numerical)
Jacobians:  11

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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2491 13618297 51585620800 191743238558025 713331744448229731 2654331885070267494400 9876826762457497608048331 36751696188633370639649025225 136753056669937085030627740091200 508858111958598842597433934752677737

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3660 227270 13848436 844583078 51520042662 3142740999758 191707325161636 11694146420296190 713342914941697980

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The isogeny class factors as 1.61.ap $\times$ 1.61.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 $\F_{61}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.61.ag_an$2$(not in LMFDB)
2.61.g_an$2$(not in LMFDB)
2.61.y_jx$2$(not in LMFDB)