Properties

Label 2.137.abp_bam
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:  $( 1 - 23 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$
Frobenius angles:  $\pm0.0596181899068$, $\pm0.220793476886$
Angle rank:  $2$ (numerical)
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13800 346600800 6608905228800 124100589740400000 2329201564749498945000 43716646168180497895219200 820517652165031129241816533800 15400296151019267674236393470400000 289048159671640449072366237697650700800 5425144911093106248850011146013826167420000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18465 2570206 352282913 48261880217 6611856717870 905824282289681 124097929393585153 17001416398277562862 2329194047515465371825

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.ax $\times$ 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.137.af_afk$2$(not in LMFDB)
2.137.f_afk$2$(not in LMFDB)
2.137.bp_bam$2$(not in LMFDB)