Properties

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

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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.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13572 345271680 6606112857552 124099018082956800 2329211643761728154052 43716691406624900890337280 820517770060087219455990918276 15400296380232310421651549933721600 289048160014235600482311471075700021968 5425144911446593104367940495836750422614400

Point counts of the (virtual) curve

$r$ 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.
TwistExtension DegreeCommon 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.
TwistExtension DegreeCommon 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)