Properties

Label 2.137.abn_zc
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:  $( 1 - 21 x + 137 x^{2} )( 1 - 18 x + 137 x^{2} )$
Frobenius angles:  $\pm0.145687313345$, $\pm0.220793476886$
Angle rank:  $2$ (numerical)
Jacobians:  36

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 36 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14040 348248160 6614267194080 124113673139414400 2329228076205097618200 43716692245537824115599360 820517720587268396688760316760 15400296233225703300927780511372800 289048159733944254232573564887030927840 5425144911056569488430413066887345053672800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18553 2572290 352320049 48262429539 6611863686766 905824357825563 124097930056017121 17001416401942187250 2329194047499778932793

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.av $\times$ 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.ad_aea$2$(not in LMFDB)
2.137.d_aea$2$(not in LMFDB)
2.137.bn_zc$2$(not in LMFDB)