Properties

Label 2.137.abp_bal
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:  $1 - 41 x + 687 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0433563628684$, $\pm0.224858212489$
Angle rank:  $2$ (numerical)
Number field:  4.0.1962053.1
Galois group:  $D_{4}$
Jacobians:  7

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 7 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13799 346561885 6608588281487 124099189615763525 2329197181830656121904 43716635330823488853808885 820517629818394757063607182903 15400296111249219264410990254333925 289048159608439587076949681562875238023 5425144910998472965726357424023121373164800

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18463 2570083 352278939 48261789402 6611855078791 905824257619735 124097929073112051 17001416394560174821 2329194047474836175118

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.1962053.1.
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_bal$2$(not in LMFDB)