Properties

Label 2.61.ay_ju
Base field $\F_{61}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
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:  $14$
Isomorphism classes:  22

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $2488$ $13594432$ $51536354872$ $191689974125568$ $713293434159593848$

Point counts of the curve

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

Jacobians and polarizations

This isogeny class contains the Jacobians of 14 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{61}$.

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.29952.1.

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)