Properties

Label 2.137.abn_yx
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:  $1 - 39 x + 647 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.103081824546$, $\pm0.245068145518$
Angle rank:  $2$ (numerical)
Number field:  4.0.12390453.1
Galois group:  $D_{4}$
Jacobians:  30

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 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14035 348053965 6612760031395 124107532259285925 2329211183281851458800 43716658602450848489147365 820517674752059353252691847115 15400296210000315204294158678962725 289048159820309423754181683797420248435 5425144911393811066450120174311378308435200

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18543 2571705 352302619 48262079514 6611858598471 905824307225013 124097929868863411 17001416407022068095 2329194047644567890318

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.12390453.1.
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_yx$2$(not in LMFDB)