Properties

Label 2.83.abe_ow
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:  $1 - 30 x + 386 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.105130850416$, $\pm0.252955120358$
Angle rank:  $2$ (numerical)
Number field:  4.0.147600.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4756 46589776 327094989124 2252784138230016 15516414026135264836 106890136255623412082896 736365241713238619816457364 5072820273437722754457822105600 34946659094473292754558392081911156 240747534255052392815606943024521215696

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6762 572058 47468686 3939135294 326940766458 27136050193698 2252292220810078 186940255561645734 15516041195712144522

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.147600.1.
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.be_ow$2$(not in LMFDB)