Properties

Label 2.61.ax_jf
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:  $1 - 23 x + 239 x^{2} - 1403 x^{3} + 3721 x^{4}$
Frobenius angles:  $\pm0.0529194219962$, $\pm0.338378256587$
Angle rank:  $2$ (numerical)
Number field:  4.0.4632645.1
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
$A(\F_{q^r})$ 2535 13656045 51546134835 191672000590005 713281995600954000 2654313006129263344125 9876823653320296055856915 36751695805098913945984889445 136753055155719811444590130269015 508858110160275873376900208127648000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 39 3671 227097 13843291 844524174 51519676223 3142740010449 191707323161011 11694146290811127 713342912420718326

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{61}$
The endomorphism algebra of this simple isogeny class is 4.0.4632645.1.
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.x_jf$2$(not in LMFDB)