Properties

Label 2.137.abn_za
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:  $1 - 39 x + 650 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.127321588991$, $\pm0.232481159802$
Angle rank:  $2$ (numerical)
Number field:  4.0.5857452.1
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
$A(\F_{q^r})$ 14038 348170476 6613664317312 124111221004924416 2329221375497132851558 43716679176721446640356352 820517704078184804000572440838 15400296230453418955160341195020288 289048159787045968000776521742334466944 5425144911234120015817411530861008377897516

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18549 2572056 352313089 48262290699 6611861710194 905824339600083 124097930033677633 17001416405065557240 2329194047576007243429

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.5857452.1.
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.bn_za$2$(not in LMFDB)