Properties

Label 2.61.ay_jy
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:  $1 - 24 x + 258 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.101801111500$, $\pm0.300249954030$
Angle rank:  $2$ (numerical)
Number field:  4.0.15424.2
Galois group:  $D_{4}$
Jacobians:  40

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 40 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2492 13626256 51602045852 191760883557376 713344109300063612 2654337966500373767824 9876828856426519717253468 36751696679537806726511345664 136753056783672385541733944655932 508858112027660653105702297431768976

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3662 227342 13849710 844597718 51520160702 3142741666046 191707327722334 11694146430022022 713342915038512302

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.15424.2.
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_jy$2$(not in LMFDB)