Properties

Label 2.61.abb_lo
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:  $1 - 27 x + 300 x^{2} - 1647 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0276619945946$, $\pm0.238460193285$
Angle rank:  $2$ (numerical)
Number field:  4.0.3757.1
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
$A(\F_{q^r})$ 2348 13374208 51446736848 191712370588672 713338783287918908 2654333741436015788032 9876817740850004802230012 36751684693040928601380384768 136753048779006607742829752009552 508858108414447470487634272540795648

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 35 3593 226658 13846209 844591415 51520078694 3142738129139 191707265197345 11694145745520074 713342909973328193

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.3757.1.
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_lo$2$(not in LMFDB)