Properties

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

Learn more about

Invariants

Base field:  $\F_{113}$
Dimension:  $2$
L-polynomial:  $( 1 - 18 x + 113 x^{2} )( 1 - 17 x + 113 x^{2} )$
Frobenius angles:  $\pm0.178616545187$, $\pm0.205038125192$
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
$A(\F_{q^r})$ 9312 161023104 2083570913664 26590557364056576 339466447350001288032 4334533460385263675375616 55347532022016346219455224928 706732550900638076953098077128704 9024267952508266514186044470728666496 115230877625090943209037627147076919812224

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 79 12609 1444018 163084865 18424878719 2081956728798 235260575910383 26584441862139649 3004041933769942354 339456738926992198689

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{113}$
The isogeny class factors as 1.113.as $\times$ 1.113.ar 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_adc$2$(not in LMFDB)
2.113.b_adc$2$(not in LMFDB)
2.113.bj_um$2$(not in LMFDB)