Properties

Label 2.137.abp_bas
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $( 1 - 21 x + 137 x^{2} )( 1 - 20 x + 137 x^{2} )$
Frobenius angles:  $\pm0.145687313345$, $\pm0.173950867407$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13806 346834332 6610806999576 124108960975107264 2329227446771918894526 43716708140160737615821056 820517770630961286601551450318 15400296327343956532405455897158400 289048159845361029115448847493354303704 5425144911081455888390209822391595943773852

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18477 2570944 352306673 48262416497 6611866090722 905824413072137 124097930814436321 17001416408495569168 2329194047510463486957

Decomposition and endomorphism algebra

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