Properties

Label 2.83.abd_ol
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:  $1 - 29 x + 375 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.172232313838$, $\pm0.237449215783$
Angle rank:  $2$ (numerical)
Number field:  4.0.336725.1
Galois group:  $D_{4}$
Jacobians:  7

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 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4829 46846129 327521955959 2253303911128061 15516900689876826064 106890467193176749684921 736365351195358717186447379 5072820175754599341929487955829 34946658867258228487713557058451601 240747533997508503295759270829493831424

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6799 572803 47479635 3939258840 326941778683 27136054228261 2252292177439539 186940254346203589 15516041179113587814

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.336725.1.
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_ol$2$(not in LMFDB)