Properties

Label 2.137.abq_bbl
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:  $1 - 42 x + 713 x^{2} - 5754 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0931478584563$, $\pm0.184503139221$
Angle rank:  $2$ (numerical)
Number field:  4.0.479808.2
Galois group:  $D_{4}$
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13687 345993673 6607972406812 124101769395764889 2329212349354414145287 43716681432499936510270096 820517732220779645642672984071 15400296289724485385115161369609193 289048159850417540615711168388585923548 5425144911225669194566207389440905852605913

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 96 18432 2569842 352286260 48262103676 6611862051366 905824370668572 124097930511292900 17001416408792986242 2329194047572379026512

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.479808.2.
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.bq_bbl$2$(not in LMFDB)