Properties

Label 2.83.abh_qv
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:  $1 - 33 x + 437 x^{2} - 2739 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0821076990436$, $\pm0.180078914894$
Angle rank:  $2$ (numerical)
Number field:  4.0.51525.2
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
$A(\F_{q^r})$ 4555 46000945 326431847605 2252373940644525 15516374481032902000 106890361098075995548705 736365522272100916162333105 5072820439732946811101747049525 34946659089926511028740376087580455 240747534127427914826869600343301088000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 51 6675 570897 47460043 3939125256 326941454175 27136060532667 2252292294643843 186940255537323621 15516041187486819750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.51525.2.
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.bh_qv$2$(not in LMFDB)