Properties

Label 2.61.aba_ld
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:  $1 - 26 x + 289 x^{2} - 1586 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.125915170111$, $\pm0.234017939091$
Angle rank:  $2$ (numerical)
Number field:  4.0.254528.3
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2399 13489577 51567838844 191809495935353 713404598749519959 2654372735023015912208 9876838226761888029162191 36751694277761747142295787753 136753052761566100401998119463516 508858109866973019957392778594903657

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3624 227190 13853220 844669336 51520835550 3142744647624 191707315193988 11694146086080174 713342912009551624

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.254528.3.
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.ba_ld$2$(not in LMFDB)