Properties

Label 2.137.abn_zb
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:  $1 - 39 x + 651 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.136074106037$, $\pm0.227156831293$
Angle rank:  $2$ (numerical)
Number field:  4.0.3737773.2
Galois group:  $D_{4}$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14039 348209317 6613965753743 124112447775085909 2329224735261325160624 43716685775813133490710013 820517712635904106146134739743 15400296232916373989622571494644037 289048159763525489715604726698849163103 5425144911152142512998588064219923491081472

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18551 2572173 352316571 48262360314 6611862708263 905824349047521 124097930053524499 17001416403682114959 2329194047540811591566

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.3737773.2.
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_zb$2$(not in LMFDB)