Properties

Label 2.137.abo_zw
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:  $1 - 40 x + 672 x^{2} - 5480 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.132371854234$, $\pm0.208023534643$
Angle rank:  $2$ (numerical)
Number field:  4.0.1159424.1
Galois group:  $D_{4}$
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13922 347520964 6612374422754 124110580288560656 2329225408221710305282 43716694404522716237378116 820517734511447549344481793218 15400296265074445936170111902941184 289048159782228653018100060016941577826 5425144911105259138097512555758032729161924

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 98 18514 2571554 352311270 48262374258 6611864013298 905824373197394 124097930312659134 17001416404782209378 2329194047520683008914

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.1159424.1.
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.bo_zw$2$(not in LMFDB)