Properties

Label 2.61.az_kr
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:  $1 - 25 x + 277 x^{2} - 1525 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.162949397008$, $\pm0.240145470170$
Angle rank:  $2$ (numerical)
Number field:  4.0.167525.1
Galois group:  $D_{4}$
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2449 13589501 51651322669 191856914855525 713423574578330704 2654376624856790081861 9876836605334808020648029 36751691781597653714814791525 136753050894563472013002363852169 508858108775768932387209686977007616

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 37 3651 227557 13856643 844691802 51520911051 3142744131697 191707302173283 11694145926427417 713342910479846806

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.167525.1.
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.z_kr$2$(not in LMFDB)