Properties

Label 2.83.abe_ov
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:  $1 - 30 x + 385 x^{2} - 2490 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.0929518943327$, $\pm0.258138369806$
Angle rank:  $2$ (numerical)
Number field:  4.0.2765376.2
Galois group:  $D_{4}$
Jacobians:  28

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 28 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 4755 46575225 327043327140 2252686441865625 15516288762724438275 106890018024823119104400 736365159881777672887588635 5072820237733104259954324115625 34946659095080745899544263011855620 240747534273234171782073804027173105625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 54 6760 571968 47466628 3939103494 326940404830 27136047178098 2252292204957508 186940255564895184 15516041196883949800

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.2765376.2.
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.be_ov$2$(not in LMFDB)