Properties

Label 2.61.ay_ju
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:  $1 - 24 x + 254 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0450812475667$, $\pm0.315976986299$
Angle rank:  $2$ (numerical)
Number field:  4.0.29952.1
Galois group:  $D_{4}$
Jacobians:  14

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 14 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2488 13594432 51536354872 191689974125568 713293434159593848 2654311386706894028608 9876817667470287006999928 36751692069434124989762715648 136753054333130915121160458463288 508858110490563947376892091662695232

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3654 227054 13844590 844537718 51519644790 3142738105790 191707303674718 11694146220469190 713342912883732774

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.29952.1.
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.y_ju$2$(not in LMFDB)