Properties

Label 2.61.ay_kb
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:  $1 - 24 x + 261 x^{2} - 1464 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.135025069903$, $\pm0.285069722533$
Angle rank:  $2$ (numerical)
Number field:  4.0.153625.1
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2495 13650145 51651330320 191813489207545 713379988161809375 2654353965383735537920 9876832369605747126082295 36751695621001444516988317545 136753055331059872566877861583120 508858111240714908267629884705590625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 38 3668 227558 13853508 844640198 51520471238 3142742783918 191707322200708 11694146305804958 713342913935332148

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.153625.1.
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_kb$2$(not in LMFDB)