Properties

Label 2.137.abo_zt
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:  $1 - 40 x + 669 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.101207174876$, $\pm0.225767625998$
Angle rank:  $2$ (numerical)
Number field:  4.0.311225.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13919 347404321 6611446830896 124106650500580121 2329213941146101601239 43716669316246173381181696 820517693531302701775636639511 15400296222811453027299914557445225 289048159790902327497482773349890376624 5425144911274303269191214651506367552262321

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18508 2571194 352300116 48262136658 6611860218862 905824327956674 124097929972097508 17001416405292383018 2329194047593259242428

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.311225.1.
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_zt$2$(not in LMFDB)