Properties

Label 2.83.abd_om
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $( 1 - 15 x + 83 x^{2} )( 1 - 14 x + 83 x^{2} )$
Frobenius angles:  $\pm0.192168636682$, $\pm0.221078141621$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4830 46860660 327571894440 2253392306272800 15516999503618647650 106890533127865261494720 736365353387823535959324210 5072820114180749092758121680000 34946658771205237652076823773877320 240747533908111018931853372230984253300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6801 572890 47481497 3939283925 326941980354 27136054309055 2252292150101233 186940253832387070 15516041173351970961

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.ap $\times$ 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.ab_abs$2$(not in LMFDB)
2.83.b_abs$2$(not in LMFDB)
2.83.bd_om$2$(not in LMFDB)