Properties

Label 2.61.ay_kd
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:  $1 - 24 x + 263 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.158141532292$, $\pm0.271682361611$
Angle rank:  $2$ (numerical)
Number field:  4.0.1106064.1
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2497 13666081 51684194452 191848285246761 713402894353668937 2654362766323998016144 9876832436132404238151073 36751692888040425554466627849 136753053010568749646587330526452 508858110073604014265980423801330801

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3672 227702 13856020 844667318 51520642062 3142742805086 191707307944804 11694146107373102 713342912299217352

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.1106064.1.
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_kd$2$(not in LMFDB)