Properties

Label 2.191.abw_bkk
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:  $1 - 48 x + 946 x^{2} - 9168 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0359858559519$, $\pm0.233419945036$
Angle rank:  $2$ (numerical)
Number field:  4.0.7488.1
Galois group:  $D_{4}$
Jacobians:  62

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 62 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28212 1315920528 48538180885428 1771204944078655488 64615053534038868452532 2357221253787748339643487888 85993798204327316064017150986548 3137139817476575237705850013946806272 114445997926579724413450865766752466626868 4175104450999212883222159649257905304669208208

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36070 6966000 1330869118 254194923024 48551219706598 9273284004033648 1771197281572939774 338298681505284405648 64615048177408841404390

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.7488.1.
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_bkk$2$(not in LMFDB)