Properties

Label 2.61.ay_jv
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:  $1 - 24 x + 255 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0628885257501$, $\pm0.312375219403$
Angle rank:  $2$ (numerical)
Number field:  4.0.3068560.1
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2489 13602385 51552775316 191707783848265 713306406880761329 2654318595792507322000 9876821171147393177461289 36751693891826492152960349385 136753055459170272616958495253236 508858111209405594391872906389034625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3656 227126 13845876 844553078 51519784718 3142739220638 191707313180836 11694146316760046 713342913891441176

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.3068560.1.
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.y_jv$2$(not in LMFDB)