Properties

Label 2.191.abw_bkj
Base Field $\F_{191}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{191}$
Dimension:  $2$
L-polynomial:  $1 - 48 x + 945 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0160200271430$, $\pm0.235843406874$
Angle rank:  $2$ (numerical)
Number field:  4.0.113737.1
Galois group:  $D_{4}$
Jacobians:  6

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 6 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28211 1315845673 48537176259584 1771197711718318537 64615016685856127984531 2357221105006202920335572992 85993797697544861123570707846739 3137139815945148767131075025248362633 114445997922222932215424545588917050153984 4175104450986650992906468097909961217328455273

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36068 6965856 1330863684 254194778064 48551216642174 9273283949383920 1771197280708311940 338298681492405868320 64615048177214430184868

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.113737.1.
All geometric endomorphisms are defined over $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

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