Properties

Label 2.83.abd_og
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:  $( 1 - 17 x + 83 x^{2} )( 1 - 12 x + 83 x^{2} )$
Frobenius angles:  $\pm0.117184483028$, $\pm0.271155063531$
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
$A(\F_{q^r})$ 4824 46773504 327272297184 2252859103835136 15516389490835992264 106890085272268210139136 736365233806656885327818664 5072820324354417375805014134784 34946659168675355889055530470236896 240747534303309562832601390300720340224

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6789 572368 47470265 3939129065 326940610518 27136049902331 2252292243416689 186940255958575024 15516041198822291589

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ar $\times$ 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.af_abm$2$(not in LMFDB)
2.83.f_abm$2$(not in LMFDB)
2.83.bd_og$2$(not in LMFDB)