Properties

Label 2.137.abo_zx
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 137 x^{2} )( 1 - 19 x + 137 x^{2} )$
Frobenius angles:  $\pm0.145687313345$, $\pm0.198575263152$
Angle rank:  $2$ (numerical)
Jacobians:  18

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 18 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13923 347559849 6612683628096 124111887406693641 2329229191974585343443 43716702492970260576915456 820517746829282002985185539747 15400296274118513324662457055480969 289048159764017139059843085536997985344 5425144911010507202635665988474794981872649

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18516 2571674 352314980 48262452658 6611865236622 905824386795874 124097930385537604 17001416403711033098 2329194047480002870836

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.av $\times$ 1.137.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 $\F_{137}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ac_aev$2$(not in LMFDB)
2.137.c_aev$2$(not in LMFDB)
2.137.bo_zx$2$(not in LMFDB)