Properties

Label 2.83.abe_os
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:  $( 1 - 18 x + 83 x^{2} )( 1 - 12 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.271155063531$
Angle rank:  $2$ (numerical)
Jacobians:  30

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 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4752 46531584 326888355024 2252392220491776 15515905884131066832 106889640601270309364736 736364864467960391709598608 5072820046643653293152232013824 34946658982361139394612697228092176 240747534196967409795215523846021325824

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6754 571698 47460430 3939006294 326939250418 27136036291698 2252292120115294 186940254961923894 15516041191968600514

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.am 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.ag_aby$2$(not in LMFDB)
2.83.g_aby$2$(not in LMFDB)
2.83.be_os$2$(not in LMFDB)