Properties

Label 2.83.abf_pn
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:  $1 - 31 x + 403 x^{2} - 2573 x^{3} + 6889 x^{4}$
Frobenius angles:  $\pm0.101476209234$, $\pm0.229218298306$
Angle rank:  $2$ (numerical)
Number field:  4.0.795821.3
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
$A(\F_{q^r})$ 4689 46407033 326923058475 2252733493647789 15516495934019559504 106890275864917346130225 736365345644157546859080111 5072820291169978109059863210069 34946659036684125576587004387745725 240747534170918087344880719193221494528

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 53 6735 571757 47467619 3939156088 326941193475 27136054023691 2252292228683059 186940255252513991 15516041190289736550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{83}$
The endomorphism algebra of this simple isogeny class is 4.0.795821.3.
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.bf_pn$2$(not in LMFDB)