Properties

Label 2.61.ax_jj
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:  $1 - 23 x + 243 x^{2} - 1403 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.100123618576$, $\pm0.325377247674$
Angle rank:  $2$ (numerical)
Number field:  4.0.103725.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2539 13687749 51609046975 191735811639909 713323953851741584 2654333127751981720725 9876831941292082696519399 36751699849411909102984461189 136753057714148488033980283701475 508858111666530911649343397895062784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 3679 227373 13847899 844573854 51520066783 3142742647629 191707344257299 11694146509589703 713342914532262454

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.103725.1.
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.x_jj$2$(not in LMFDB)