Properties

Label 2.137.abn_ys
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:  $( 1 - 23 x + 137 x^{2} )( 1 - 16 x + 137 x^{2} )$
Frobenius angles:  $\pm0.0596181899068$, $\pm0.260462969152$
Angle rank:  $2$ (numerical)
Jacobians:  12

This isogeny class is not 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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 14030 347859820 6611252965760 124101356231776000 2329193819846267117150 43716621717253382549048320 820517613609600290037191330270 15400296131508547450262137325952000 289048159745799821196426261963113502080 5425144911344216853068247136261704255981100

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 99 18533 2571120 352285089 48261719739 6611853019826 905824239725763 124097929236364801 17001416402639515440 2329194047623275455093

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The isogeny class factors as 1.137.ax $\times$ 1.137.aq and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.ah_adq$2$(not in LMFDB)
2.137.h_adq$2$(not in LMFDB)
2.137.bn_ys$2$(not in LMFDB)