Properties

Label 2.83.abe_ou
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:  $1 - 30 x + 384 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0801876089965$, $\pm0.262835026667$
Angle rank:  $2$ (numerical)
Number field:  4.0.2900800.5
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4754 46560676 326991667466 2252588556793936 15516162317924403914 106889896008114854003716 736365069753205810960642706 5072820188134591150546801996800 34946659076910001812623996204404034 240747534270345644705223431873360635396

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6758 571878 47464566 3939071394 326940031622 27136043856738 2252292182936158 186940255467694374 15516041196697785878

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.2900800.5.
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_ou$2$(not in LMFDB)