Properties

Label 2.137.abq_bbi
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $1 - 42 x + 710 x^{2} - 5754 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0387594407114$, $\pm0.204006140474$
Angle rank:  $2$ (numerical)
Number field:  4.0.39600.1
Galois group:  $D_{4}$
Jacobians:  12

This isogeny class is simple and geometrically 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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13684 345876784 6606998222836 124097319488330496 2329197815680791488884 43716643676903369178871216 820517650277001837983016620404 15400296137895869596701921316614144 289048159609537543091930575351321032244 5425144910903940809160689567253233459253424

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 96 18426 2569464 352273630 48261802536 6611856341082 905824280205360 124097929287834814 17001416394624755088 2329194047434250395386

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.39600.1.
All geometric endomorphisms are defined over $\F_{137}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.bq_bbi$2$(not in LMFDB)