Properties

Label 2.61.aba_kz
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:  $1 - 26 x + 285 x^{2} - 1586 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0471438380502$, $\pm0.263959254932$
Angle rank:  $2$ (numerical)
Number field:  4.0.406080.2
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
$A(\F_{q^r})$ 2395 13457505 51496571500 191723273550345 713333008278344875 2654328145571392554000 9876816969737645331500755 36751686872946600285796668105 136753051281438354671922321071500 508858110023359866417821883195332625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 36 3616 226878 13846996 844584576 51519970078 3142737883776 191707276568356 11694145959510198 713342912228782576

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.406080.2.
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.ba_kz$2$(not in LMFDB)