Properties

Label 2.83.abe_ox
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$
Frobenius angles:  $\pm0.117184483028$, $\pm0.247123549255$
Angle rank:  $2$ (numerical)
Jacobians:  6

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 contains the Jacobians of 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4757 46604329 327146653424 2252881645896361 15516538108163352557 106890250704441809403136 736365315281780918814022373 5072820295401368456891547456009 34946659075554323802361365784296176 240747534216889191307285836642250009849

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6764 572148 47470740 3939166794 326941116518 27136052904798 2252292230561764 186940255460442444 15516041193252547964

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ar $\times$ 1.83.an 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.ae_acd$2$(not in LMFDB)
2.83.e_acd$2$(not in LMFDB)
2.83.be_ox$2$(not in LMFDB)