Properties

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

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Invariants

Base field:  $\F_{163}$
Dimension:  $2$
L-polynomial:  $1 - 43 x + 777 x^{2} - 7009 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0736354163852$, $\pm0.248401776572$
Angle rank:  $2$ (numerical)
Number field:  4.0.276525.1
Galois group:  $D_{4}$
Jacobians:  56

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 56 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20295 698127705 18754065411345 498326351830458525 13239661121401530618000 351763863370032679079417145 9346014526376741640480285017445 248314265131097475273903930044997525 6597461723417174376661225725449764048395 175287960541068079194656455956363662704992000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 121 26275 4330447 705932923 115063835656 18755368264375 3057125171182357 498311413297416643 81224760529363607431 13239635967162211519750

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.276525.1.
All geometric endomorphisms are defined over $\F_{163}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.163.br_bdx$2$(not in LMFDB)