Properties

Label 2.83.abg_qc
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:  $( 1 - 18 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$
Frobenius angles:  $\pm0.0496118990883$, $\pm0.221078141621$
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
$A(\F_{q^r})$ 4620 46181520 326592868140 2252372482483200 15516157023790985100 106889979649503276792720 736365090742912639181383980 5072820071165601760849677926400 34946658850885961879384057167876620 240747534025176412624754269447068819600

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 52 6702 571180 47460014 3939070052 326940287454 27136044630236 2252292131002846 186940254258623380 15516041180896768782

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.as $\times$ 1.83.ao 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_adi$2$(not in LMFDB)
2.83.e_adi$2$(not in LMFDB)
2.83.bg_qc$2$(not in LMFDB)