Properties

Label 2.137.abn_yr
Base field $\F_{137}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{137}$
Dimension:  $2$
L-polynomial:  $1 - 39 x + 641 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0483327645413$, $\pm0.263061961588$
Angle rank:  $2$ (numerical)
Number field:  4.0.10441053.1
Galois group:  $D_{4}$
Jacobians:  $12$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $14029$ $347820997$ $6610951564213$ $124100116808417829$ $2329190290697469620224$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $99$ $18531$ $2571003$ $352281571$ $48261646614$ $6611851845123$ $905824224180051$ $124097929055158339$ $17001416400566702139$ $2329194047596845024366$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{137}$.

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.10441053.1.

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_yr$2$(not in LMFDB)