Properties

Label 2.137.abn_yw
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:  $1 - 39 x + 646 x^{2} - 5343 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0951044323561$, $\pm0.248558856465$
Angle rank:  $2$ (numerical)
Number field:  4.0.14039388.1
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
$A(\F_{q^r})$ 14034 348015132 6612458610528 124106299865636544 2329207748235794776674 43716651485097617084659968 820517663754082530579602722098 15400296198780343185567313769663232 289048159818652721233520939228213244768 5425144911416729341366871438135347704306972

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18541 2571588 352299121 48262008339 6611857522018 905824295083611 124097929778451169 17001416406924623124 2329194047654407463341

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.14039388.1.
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_yw$2$(not in LMFDB)