Properties

Label 2.137.abr_bcf
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:  $1 - 43 x + 733 x^{2} - 5891 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0303922480591$, $\pm0.181717955123$
Angle rank:  $2$ (numerical)
Number field:  4.0.134693.2
Galois group:  $D_{4}$
Jacobians:  5

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 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 13569 345154653 6605115336873 124094305960546869 2329195549979480135424 43716647148181087668694461 820517666948127100141815680337 15400296171781308207825317473728933 289048159646232912499352644539909920169 5425144910886092372837139103971961535705088

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 95 18387 2568731 352265075 48261755590 6611856866091 905824298609731 124097929560888835 17001416396783126399 2329194047426587471662

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.134693.2.
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.br_bcf$2$(not in LMFDB)