Properties

Label 2.61.abb_lr
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:  $1 - 27 x + 303 x^{2} - 1647 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.114657586013$, $\pm0.208688212581$
Angle rank:  $2$ (numerical)
Number field:  4.0.68725.1
Galois group:  $D_{4}$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2351 13398349 51502277891 191783445050389 713402752074698576 2654378422548308711725 9876842969484423503105891 36751696291753030273499928549 136753053010772993424220348275311 508858109538775094332170971988093184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 35 3599 226901 13851339 844667150 51520945943 3142746156725 191707325699539 11694146107390571 713342911549467254

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.68725.1.
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.bb_lr$2$(not in LMFDB)