Properties

Label 2.83.abd_oe
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:  $1 - 29 x + 368 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0975278333375$, $\pm0.279698317393$
Angle rank:  $2$ (numerical)
Number field:  4.0.6473016.1
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
$A(\F_{q^r})$ 4822 46744468 327172449256 2252679859352224 15516177016952599882 106889908048472760894400 736365136568554375624735258 5072820306825460091954388983424 34946659198143966978246324635040904 240747534343142713625632643047878814228

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6785 572194 47466489 3939075125 326940068450 27136046318975 2252292235633969 186940256116211542 15516041201389515425

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.6473016.1.
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_oe$2$(not in LMFDB)