# Properties

 Label 2.137.abr_bci Base Field $\F_{137}$ Dimension $2$ Ordinary Yes $p$-rank $2$ Principally polarizable Yes Contains a Jacobian No

## Invariants

 Base field: $\F_{137}$ Dimension: $2$ L-polynomial: $( 1 - 22 x + 137 x^{2} )( 1 - 21 x + 137 x^{2} )$ Frobenius angles: $\pm0.111017258455$, $\pm0.145687313345$ 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 $A(\F_{q^r})$ 13572 345271680 6606112857552 124099018082956800 2329211643761728154052 43716691406624900890337280 820517770060087219455990918276 15400296380232310421651549933721600 289048160014235600482311471075700021968 5425144911446593104367940495836750422614400

 $r$ 1 2 3 4 5 6 7 8 9 10 $C(\F_{q^r})$ 95 18393 2569118 352278449 48262089055 6611863559886 905824412441911 124097931240618721 17001416418428539886 2329194047667228963993

## Decomposition and endomorphism algebra

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

## Base change

This is a primitive isogeny class.

## Twists

Below are some of the twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ab_ahg $2$ (not in LMFDB) 2.137.b_ahg $2$ (not in LMFDB) 2.137.br_bci $2$ (not in LMFDB)
Below is a list of all twists of this isogeny class.
 Twist Extension Degree Common base change 2.137.ab_ahg $2$ (not in LMFDB) 2.137.b_ahg $2$ (not in LMFDB) 2.137.br_bci $2$ (not in LMFDB) 2.137.abd_ra $4$ (not in LMFDB) 2.137.an_ec $4$ (not in LMFDB) 2.137.n_ec $4$ (not in LMFDB) 2.137.bd_ra $4$ (not in LMFDB)