Properties

Label 2.83.abd_ok
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:  $( 1 - 16 x + 83 x^{2} )( 1 - 13 x + 83 x^{2} )$
Frobenius angles:  $\pm0.158801688027$, $\pm0.247123549255$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4828 46831600 327472019728 2253215327224000 15516800734120996948 106890397780558291513600 736365341951872008618709444 5072820226899067530766745568000 34946658951931111796882619351319312 240747534078666415729767222676943398000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6797 572716 47477769 3939233465 326941566374 27136053887627 2252292200147281 186940254799144468 15516041184344168957

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The isogeny class factors as 1.83.aq $\times$ 1.83.an 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.ad_abq$2$(not in LMFDB)
2.83.d_abq$2$(not in LMFDB)
2.83.bd_ok$2$(not in LMFDB)