Properties

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

Learn more about

Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 17 x + 83 x^{2} )( 1 - 15 x + 83 x^{2} )$
Frobenius angles:  $\pm0.117184483028$, $\pm0.192168636682$
Angle rank:  $2$ (numerical)
Jacobians:  9

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 9 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4623 46225377 326758299984 2252716875293049 15516663756749536623 106890561952325735291136 736365634304534154407843751 5072820483596500624608450520425 34946659092049460912905379232668496 240747534109364510780325257185874751777

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 52 6708 571468 47467268 3939198692 326942068518 27136064661212 2252292314118916 186940255548679924 15516041186322643668

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ar $\times$ 1.83.ap 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.ac_adl$2$(not in LMFDB)
2.83.c_adl$2$(not in LMFDB)
2.83.bg_qf$2$(not in LMFDB)