Properties

Label 2.139.abo_zy
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $( 1 - 22 x + 139 x^{2} )( 1 - 18 x + 139 x^{2} )$
Frobenius angles:  $\pm0.117174211439$, $\pm0.223543330897$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14396 368480016 7213089440924 139365886709412864 2692480546039269410876 52020910635863569160821776 1005095251460868698109388050716 19419444585503731375027728846372864 375203088444644310891543437499454555964 7249298871918277367680609351722032861807376

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 100 19070 2685820 373333774 51889390900 7212555180686 1002544409117260 139353667356344734 19370159742301145860 2692452204209313701150

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.aw $\times$ 1.139.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 $\F_{139}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.139.ae_aeo$2$(not in LMFDB)
2.139.e_aeo$2$(not in LMFDB)
2.139.bo_zy$2$(not in LMFDB)