Properties

Label 2.137.abp_ban
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:  $1 - 41 x + 689 x^{2} - 5617 x^{3} + 18769 x^{4}$
Frobenius angles:  $\pm0.0733101034139$, $\pm0.216316581678$
Angle rank:  $2$ (numerical)
Number field:  4.0.2725821.1
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
$A(\F_{q^r})$ 13801 346639717 6609222180241 124101988459622629 2329205927883038252176 43716656860064202894261781 820517673765549289685334113953 15400296187796326720391406051416325 289048159724869233139902893496745280809 5425144911159123794239975148118245887639552

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 97 18467 2570329 352286883 48261970622 6611858334947 905824306135937 124097929689940291 17001416401408406953 2329194047543808886382

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{137}$
The endomorphism algebra of this simple isogeny class is 4.0.2725821.1.
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_ban$2$(not in LMFDB)