Properties

Label 2.113.abk_vc
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:  $1 - 36 x + 548 x^{2} - 4068 x^{3} + 12769 x^{4}$
Frobenius angles:  $\pm0.133628584847$, $\pm0.215153007500$
Angle rank:  $2$ (numerical)
Number field:  4.0.10496.2
Galois group:  $D_{4}$
Jacobians:  22

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 22 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 9214 160526308 2082421357150 26588663941374864 339464120671168237054 4334531649110267770708900 55347532397544492163913866846 706732555594288326290379829776384 9024267963335441940149649089878861150 115230877642269502876473215779547796558628

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 78 12570 1443222 163073254 18424752438 2081955858810 235260577506606 26584442038695934 3004041937374144846 339456738977598233850

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The endomorphism algebra of this simple isogeny class is 4.0.10496.2.
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_vc$2$(not in LMFDB)