Properties

Label 2.113.abk_ux
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $1 - 36 x + 543 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.0767197926682$, $\pm0.243129589180$
Angle rank:  $2$ (numerical)
Number field:  4.0.4366096.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9209 160393153 2081640116900 26586216166081609 339458847565054347929 4334523129051568208928400 55347522027297128869313461721 706732547172296478822270111000969 9024267962388134321732961428871404900 115230877653864426154459514964226946713153

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12560 1442682 163058244 18424466238 2081951766470 235260533426766 26584441721894404 3004041937058800506 339456739011755526800

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.4366096.1.
All geometric endomorphisms are defined over $\F_{113}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.113.bk_ux$2$(not in LMFDB)