Properties

Label 2.137.abp_bak
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:  $1 - 41 x + 686 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0179276178433$, $\pm0.228596896516$
Angle rank:  $2$ (numerical)
Number field:  4.0.448668.1
Galois group:  $D_{4}$
Jacobians:  2

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 2 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13798 346522972 6608271338296 124097788085696704 2329192779126488895478 43716624347913816886705408 820517606724080334269317926502 15400296068470250290976354969555712 289048159535154087608804116889119628152 5425144910874606289843272163751621845815772

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18461 2569960 352274961 48261698177 6611853417698 905824232124377 124097928728392609 17001416390249622232 2329194047421656116541

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.448668.1.
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_bak$2$(not in LMFDB)