# Properties

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

## 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.

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

 $r$ 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.
 Twist Extension Degree Common 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)