Properties

Label 2.83.abj_se
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 18 x + 83 x^{2} )( 1 - 17 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.117184483028$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4422 45555444 325781705304 2251697357185056 15515821295150911482 106890008473814497753536 736365371659523060976040938 5072820440581350160226821989504 34946659171730185871758945594996536 240747534226429904571087257578637089524

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 49 6609 569758 47445785 3938984819 326940375618 27136054982393 2252292295020529 186940255974916234 15516041193867441489

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.ar and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
All geometric endomorphisms are defined over $\F_{83}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.83.ab_afk$2$(not in LMFDB)
2.83.b_afk$2$(not in LMFDB)
2.83.bj_se$2$(not in LMFDB)