Properties

Label 2.163.abt_bfs
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:  $1 - 45 x + 824 x^{2} - 7335 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0358759288257$, $\pm0.220913488148$
Angle rank:  $2$ (numerical)
Number field:  4.0.2395800.1
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
$A(\F_{q^r})$ 20014 695966836 18747185129896 498312683291570976 13239643863120727830514 351763845979029885856517056 9346014453180684556209980781826 248314264679551646851613806487068800 6597461721545554198792882623305611608904 175287960535440378599122587675251444444958196

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 26193 4328858 705913561 115063685669 18755367337122 3057125147239583 498311412391264753 81224760506321124254 13239635966737146917553

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.2395800.1.
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.bt_bfs$2$(not in LMFDB)