Properties

Label 2.137.abo_zs
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:  $1 - 40 x + 668 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0914703999019$, $\pm0.230187862161$
Angle rank:  $2$ (numerical)
Number field:  4.0.6084864.2
Galois group:  $D_{4}$
Jacobians:  12

This isogeny class is simple and geometrically 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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13918 347365444 6611137641646 124105337760005776 2329210080181838052718 43716660678911497038452356 820517678523967945871695217182 15400296203629966883554562635567104 289048159778131942752232104525773522494 5425144911290463643639078744212515932033924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18506 2571074 352296390 48262056658 6611858912522 905824311389074 124097929817530174 17001416404541246498 2329194047600197425386

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.6084864.2.
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.bo_zs$2$(not in LMFDB)