Properties

Label 2.163.abt_bft
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:  $1 - 45 x + 825 x^{2} - 7335 x^{3} + 26569 x^{4}$
Frobenius angles:  $\pm0.0521334521506$, $\pm0.217387748284$
Angle rank:  $2$ (numerical)
Number field:  4.0.3785341.1
Galois group:  $D_{4}$
Jacobians:  24

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 24 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 20015 696021625 18747770750345 498316073399828125 13239657817526454753200 351763891573583642346909625 9346014578250550963865693903405 248314264978346769555751525146703125 6597461722190028935173450538665221753635 175287960536761524851540487092839794114400000

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 119 26195 4328993 705918363 115063806944 18755369768135 3057125188150523 498311412990880003 81224760514255585769 13239635966836934121350

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{163}$
The endomorphism algebra of this simple isogeny class is 4.0.3785341.1.
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_bft$2$(not in LMFDB)