Properties

Label 2.83.abd_oi
Base Field $\F_{83}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{83}$
Dimension:  $2$
L-polynomial:  $1 - 29 x + 372 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.136898030827$, $\pm0.260828041475$
Angle rank:  $2$ (numerical)
Number field:  4.0.2957048.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4826 46802548 327372153992 2253037593101984 15516597396542903926 106890248505828100770496 736365302179623000634827878 5072820297334333468970771043968 34946659085509655042151092509843496 240747534212757845957636156106323531188

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6793 572542 47474025 3939181845 326941109794 27136052421967 2252292231419985 186940255513696522 15516041192986285113

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.2957048.1.
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_oi$2$(not in LMFDB)