Properties

Label 2.163.abs_bfe
Base Field $\F_{163}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $( 1 - 22 x + 163 x^{2} )^{2}$
Frobenius angles:  $\pm0.169471200781$, $\pm0.169471200781$
Angle rank:  $1$ (numerical)
Jacobians:  32

This isogeny class is not 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 32 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20164 697593744 18756331016164 498351193239684096 13239774480732511599364 351764212452980009136579216 9346015304071806209233753988644 248314266255688156522375661921255424 6597461723549936594946605249687625801796 175287960535661549493786405009143859510363024

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26254 4330968 705968110 115064820840 18755386876798 3057125425570056 498311415554219614 81224760530998111704 13239635966753852127214

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The isogeny class factors as 1.163.aw 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-42}) \)$)$
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_agc$2$(not in LMFDB)
2.163.bs_bfe$2$(not in LMFDB)
2.163.w_mj$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.a_agc$2$(not in LMFDB)
2.163.bs_bfe$2$(not in LMFDB)
2.163.w_mj$3$(not in LMFDB)
2.163.a_gc$4$(not in LMFDB)
2.163.aw_mj$6$(not in LMFDB)