Properties

Label 2.61.ax_je
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:  $1 - 23 x + 238 x^{2} - 1403 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0340660663953$, $\pm0.341309165886$
Angle rank:  $2$ (numerical)
Number field:  4.0.2213900.2
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
$A(\F_{q^r})$ 2534 13648124 51530410400 191655910377344 713271020537225934 2654307120235994182400 9876820571893517799834494 36751693894297841674955984384 136753053861788496390289098250400 508858109366293898619741186438165084

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 3669 227028 13842129 844511179 51519561978 3142739029959 191707313193729 11694146180163348 713342911307674429

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.2213900.2.
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.x_je$2$(not in LMFDB)