Properties

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

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 113 x^{2} )( 1 - 18 x + 113 x^{2} )$
Frobenius angles:  $\pm0.0498602789898$, $\pm0.178616545187$
Angle rank:  $2$ (numerical)
Jacobians:  7

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 contains the Jacobians of 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 8928 159096960 2079252955008 26583666961420800 339457916682754407648 4334525412248450170920960 55347527268266932222499849184 706732551891434700776371275417600 9024267960046823190201538832157916032 115230877637388224888831714218660042396800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 75 12457 1441026 163042609 18424415715 2081952863134 235260555704067 26584441899409441 3004041936279413538 339456738963218557657

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.av $\times$ 1.113.as 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.ad_afw$2$(not in LMFDB)
2.113.d_afw$2$(not in LMFDB)
2.113.bn_xg$2$(not in LMFDB)