Properties

Label 2.83.abd_oj
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:  $1 - 29 x + 373 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.147367193729$, $\pm0.254584002254$
Angle rank:  $2$ (numerical)
Number field:  4.0.1911221.1
Galois group:  $D_{4}$
Jacobians:  16

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 4827 46817073 327422085741 2253126554551629 15516699636345046032 106890324886084018323825 736365325624310924440938393 5072820267472799619989192916789 34946659024817455128940162427314359 240747534150709945689729710860515395328

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6795 572629 47475899 3939207800 326941343415 27136053285935 2252292218161699 186940255189035577 15516041188987333350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.1911221.1.
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.bd_oj$2$(not in LMFDB)