Properties

Label 2.83.abd_od
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:  $1 - 29 x + 367 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0872026692841$, $\pm0.283516371812$
Angle rank:  $2$ (numerical)
Number field:  4.0.6676613.1
Galois group:  $D_{4}$
Jacobians:  17

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 17 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4821 46729953 327122528607 2252589953882589 15516069066930023376 106889814180422538476841 736365077042446036298984043 5072820281000287069645939657653 34946659191710413476310428031395321 240747534341768212905853775980606111488

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6783 572107 47464595 3939047720 326939781339 27136044125357 2252292224167795 186940256081796517 15516041201300929638

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.6676613.1.
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_od$2$(not in LMFDB)