Properties

Label 2.137.abo_zu
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:  $( 1 - 22 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$
Frobenius angles:  $\pm0.111017258455$, $\pm0.220793476886$
Angle rank:  $2$ (numerical)
Jacobians:  100

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 contains the Jacobians of 100 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13920 347443200 6611756024160 124107961835520000 2329217782807488309600 43716677816240030336716800 820517707863979692153919839840 15400296239435980287083188715520000 289048159795773569922802694284313309280 5425144911237691373986986507475366279680000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18510 2571314 352303838 48262216258 6611861504430 905824343779474 124097930106060478 17001416405578902818 2329194047577540545550

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.aw $\times$ 1.137.as 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.ae_aes$2$(not in LMFDB)
2.137.e_aes$2$(not in LMFDB)
2.137.bo_zu$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ae_aes$2$(not in LMFDB)
2.137.e_aes$2$(not in LMFDB)
2.137.bo_zu$2$(not in LMFDB)
2.137.aba_qc$4$(not in LMFDB)
2.137.ak_fa$4$(not in LMFDB)
2.137.k_fa$4$(not in LMFDB)
2.137.ba_qc$4$(not in LMFDB)