Properties

Label 2.137.abp_bar
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:  $1 - 41 x + 693 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.125334691278$, $\pm0.189503359060$
Angle rank:  $2$ (numerical)
Number field:  4.0.347525.1
Galois group:  $D_{4}$
Jacobians:  11

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 11 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13805 346795405 6610490027405 124107569282705525 2329223182564580962000 43716698174453164852524445 820517752737636596668538311205 15400296305293084786293157377239525 289048159840309511271395468212681136405 5425144911149320948717116537228772828672000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18475 2570821 352302723 48262328142 6611864583475 905824393318501 124097930636747043 17001416408198445817 2329194047539600200750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.347525.1.
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.bp_bar$2$(not in LMFDB)