Properties

Label 2.191.abz_bno
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:  $1 - 51 x + 1028 x^{2} - 9741 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0240713736749$, $\pm0.177822725834$
Angle rank:  $2$ (numerical)
Number field:  4.0.270504.1
Galois group:  $D_{4}$
Jacobians:  4

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 4 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27718 1311116836 48519254825752 1771164416850588576 64615050886962155727298 2357221626132998760043215424 85993799931149352921344523081922 3137139821959443459332799921150885504 114445997931413107046476929390998695144312 4175104450980470191127129159624398411299113476

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 141 35937 6963282 1330838665 254194912611 48551227375722 9273284190248373 1771197284103921649 338298681519571728942 64615048177118774421177

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.270504.1.
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.bz_bno$2$(not in LMFDB)