Properties

Label 2.83.abg_qd
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:  $1 - 32 x + 419 x^{2} - 2656 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0738974052033$, $\pm0.213660075367$
Angle rank:  $2$ (numerical)
Number field:  4.0.325008.5
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4621 46196137 326648009572 2252487468544729 15516327194810226301 106890178131336890072848 736365282543118719755324677 5072820228711543270625370859177 34946658962680188204812383889458372 240747534095305033566146236755060748297

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 52 6704 571276 47462436 3939113252 326940894542 27136051698332 2252292200952004 186940254856644532 15516041185416518384

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.325008.5.
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.bg_qd$2$(not in LMFDB)