Properties

Label 2.61.az_ko
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:  $1 - 25 x + 274 x^{2} - 1525 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.117879759240$, $\pm0.267042325912$
Angle rank:  $2$ (numerical)
Number field:  4.0.1247324.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 2446 13565516 51599945224 191798815331264 713380815074539126 2654355765983016632576 9876831820505129274291766 36751694251425207381173176064 136753054567597396570376637505864 508858111254263699197475852698176876

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 37 3645 227332 13852449 844641177 51520506186 3142742609197 191707315056609 11694146240519092 713342913954325525

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.1247324.2.
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_ko$2$(not in LMFDB)