Properties

Label 2.113.abn_xi
Base Field $\F_{113}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 20 x + 113 x^{2} )( 1 - 19 x + 113 x^{2} )$
Frobenius angles:  $\pm0.110150159186$, $\pm0.148111132014$
Angle rank:  $2$ (numerical)
Jacobians:  0

This isogeny class is not simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

This isogeny class is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8930 159150460 2079591681440 26584862067467200 339460963390899099650 4334531653823464409854720 55347538064423423022131434610 706732567999365850480768214880000 9024267980793842192578591072385225120 115230877659853536237764329224342211402300

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 12461 1441260 163049937 18424581075 2081955861074 235260601594275 26584442505325153 3004041943185781500 339456739029398747261

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.au $\times$ 1.113.at and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ab_afy$2$(not in LMFDB)
2.113.b_afy$2$(not in LMFDB)
2.113.bn_xi$2$(not in LMFDB)