Properties

Label 2.137.abp_bao
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:  $1 - 41 x + 690 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0859306910897$, $\pm0.211296820890$
Angle rank:  $2$ (numerical)
Number field:  4.0.2343212.1
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
$A(\F_{q^r})$ 13802 346678636 6609539135816 124103385773447936 2329210271231295013402 43716667406553962868800512 820517694621509077415764409306 15400296221596321646220073271241728 289048159768238348259926978539351199432 5425144911197141292293425243443830592476716

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18469 2570452 352290849 48262060617 6611859930034 905824329160225 124097929962305793 17001416403959318836 2329194047560131055029

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.2343212.1.
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_bao$2$(not in LMFDB)