# Properties

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

## 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.

 $r$ 1 2 3 4 5 6 7 8 9 10 $A(\F_{q^r})$ 14042 366243444 7207243370936 139356758471807520 2692475295239121032102 52020929015322887512622016 1005095326938601487011833933782 19419444751110424532259464549911680 375203088691203209202844099724099775896 7249298872122176521644227772274726352706804

 $r$ 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.
 Twist Extension Degree Common 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)