Properties

Label 2.83.abc_ni
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:  $( 1 - 18 x + 83 x^{2} )( 1 - 10 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.315076740302$
Angle rank:  $2$ (numerical)
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4884 46827792 327019555764 2252208505181184 15515573444515367124 106889433811913573534736 736364907019614503009330292 5072820244747059012882175180800 34946659153045064323820174053169556 240747534230357623274324477578046279952

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 56 6798 571928 47456558 3938921896 326938617918 27136037859784 2252292208071646 186940255874963864 15516041194120580718

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.ak 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.ai_ao$2$(not in LMFDB)
2.83.i_ao$2$(not in LMFDB)
2.83.bc_ni$2$(not in LMFDB)