Properties

Label 2.163.abs_bet
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:  $1 - 44 x + 799 x^{2} - 7172 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0415917694910$, $\pm0.238728410361$
Angle rank:  $2$ (numerical)
Number field:  4.0.6491408.1
Galois group:  $D_{4}$
Jacobians:  12

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 12 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20153 696991505 18750032701988 498316045500751625 13239638037633233537073 351763807232181126348139280 9346014361142046131566951283369 248314264611329347518462135381847625 6597461721911244164043119996177194363652 175287960537308909461962135815904512255153025

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 120 26232 4329516 705918324 115063635040 18755365271214 3057125117133312 498311412254357796 81224760510823322388 13239635966878278506632

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.6491408.1.
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.bs_bet$2$(not in LMFDB)