Properties

Label 2.191.abx_blr
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:  $1 - 49 x + 979 x^{2} - 9359 x^{3} + 36481 x^{4}$
Frobenius angles:  $\pm0.0994375871297$, $\pm0.193329123011$
Angle rank:  $2$ (numerical)
Number field:  4.0.3034733.1
Galois group:  $D_{4}$
Jacobians:  17

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 17 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28053 1314816057 48538603353267 1771240131525873213 64615300826758128722448 2357222367756745896371923113 85993802015284144409102086368303 3137139827788087928698968854912226453 114445997948200625147826147668171970028113 4175104451030273748542396365103545992727372032

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36039 6966059 1330895555 254195895868 48551242650795 9273284414994505 1771197287394715123 338298681569195091425 64615048177889547775374

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The endomorphism algebra of this simple isogeny class is 4.0.3034733.1.
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.bx_blr$2$(not in LMFDB)