Properties

Label 2.61.ay_ke
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:  $1 - 24 x + 264 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.171237183552$, $\pm0.262983076991$
Angle rank:  $2$ (numerical)
Number field:  4.0.540928.1
Galois group:  $D_{4}$
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2498 13674052 51700628882 191865600966928 713414043543619298 2654366609156780277508 9876831796222033004396978 36751690937961966776395235328 136753051487209857317371980182978 508858109352033064236296786483934532

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3674 227774 13857270 844680518 51520716650 3142742601470 191707297772638 11694145977106310 713342911287682874

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.540928.1.
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_ke$2$(not in LMFDB)