Properties

Label 2.83.abe_oy
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:  $1 - 30 x + 388 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.129569760154$, $\pm0.240369587858$
Angle rank:  $2$ (numerical)
Number field:  4.0.1168704.1
Galois group:  $D_{4}$
Jacobians:  26

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 26 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4758 46618884 327198320046 2252978964873936 15516661008815216718 106890361375204429418916 736365380621596860886660662 5072820303776855089842027869184 34946659038789309097845035921019654 240747534159826509503144094006179129124

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6766 572238 47472790 3939197994 326941455022 27136055312658 2252292234280414 186940255263775254 15516041189574890686

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.1168704.1.
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.be_oy$2$(not in LMFDB)