Properties

Label 2.137.abn_yq
Base Field $\F_{137}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $1 - 39 x + 640 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0341358853414$, $\pm0.265546250536$
Angle rank:  $2$ (numerical)
Number field:  4.0.1533528.4
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
$A(\F_{q^r})$ 14028 347782176 6610650166512 124098875979071616 2329186742728070020908 43716606053161505900470272 820517584825041745214691502188 15400296084237505749966804210344448 289048159668318375183867069581808643824 5425144911202759242891602368975851838998816

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18529 2570886 352278049 48261573099 6611850650734 905824207948563 124097928855447553 17001416398082163030 2329194047562543026929

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.1533528.4.
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.bn_yq$2$(not in LMFDB)