Properties

Label 2.61.abb_lp
Base Field $\F_{61}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{61}$
Dimension:  $2$
L-polynomial:  $1 - 27 x + 301 x^{2} - 1647 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0643104250482$, $\pm0.230612073966$
Angle rank:  $2$ (numerical)
Number field:  4.0.2197.1
Galois group:  $C_4$
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2349 13382253 51465248721 191736116755173 713360334091993344 2654349124865794486533 9876826880985021723038529 36751689407267707434417008037 136753051001877533214507350737269 508858109453949447444325201111339008

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 35 3595 226739 13847923 844616930 51520377283 3142741037471 191707289788099 11694145935604151 713342911430554390

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.2197.1.
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_lp$2$(not in LMFDB)