Properties

Label 2.139.abr_bcm
Base Field $\F_{139}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{139}$
Dimension:  $2$
L-polynomial:  $( 1 - 22 x + 139 x^{2} )( 1 - 21 x + 139 x^{2} )$
Frobenius angles:  $\pm0.117174211439$, $\pm0.150285916016$
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
$A(\F_{q^r})$ 14042 366243444 7207243370936 139356758471807520 2692475295239121032102 52020929015322887512622016 1005095326938601487011833933782 19419444751110424532259464549911680 375203088691203209202844099724099775896 7249298872122176521644227772274726352706804

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18953 2683642 373309321 51889289707 7212557728946 1002544484403433 139353668544736081 19370159755029946318 2692452204285043607753

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{139}$
The isogeny class factors as 1.139.aw $\times$ 1.139.av 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.ab_ahc$2$(not in LMFDB)
2.139.b_ahc$2$(not in LMFDB)
2.139.br_bcm$2$(not in LMFDB)