Properties

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

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 22 x + 137 x^{2} )( 1 - 20 x + 137 x^{2} )$
Frobenius angles:  $\pm0.111017258455$, $\pm0.173950867407$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13688 346032640 6608297143352 124103249888051200 2329217153377091196728 43716693710857697597217280 820517757907671806068415624312 15400296333554233556514706882560000 289048159907190344829510762934876984568 5425144911262577773947614111142999329651200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 96 18434 2569968 352290462 48262203216 6611863908386 905824399026048 124097930864479678 17001416412132284736 2329194047588225099714

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.aw $\times$ 1.137.au 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.ac_agk$2$(not in LMFDB)
2.137.c_agk$2$(not in LMFDB)
2.137.bq_bbm$2$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.ac_agk$2$(not in LMFDB)
2.137.c_agk$2$(not in LMFDB)
2.137.bq_bbm$2$(not in LMFDB)
2.137.abc_qs$4$(not in LMFDB)
2.137.am_ek$4$(not in LMFDB)
2.137.m_ek$4$(not in LMFDB)
2.137.bc_qs$4$(not in LMFDB)