Properties

Label 2.83.abd_oh
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:  $1 - 29 x + 371 x^{2} - 2407 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.126930498020$, $\pm0.266276878158$
Angle rank:  $2$ (numerical)
Number field:  4.0.4038237.1
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
$A(\F_{q^r})$ 4825 46788025 327322224475 2252948442866125 15516494014708546000 106890168635864748551425 736365271584755794691811775 5072820316342098835543789303125 34946659133598937103591920850295925 240747534263922428917725745117234912000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 55 6791 572455 47472147 3939155600 326940865499 27136051294505 2252292239859283 186940255770940645 15516041196283813286

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.4038237.1.
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_oh$2$(not in LMFDB)