Properties

Label 2.191.aby_bmt
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:  $( 1 - 25 x + 191 x^{2} )^{2}$
Frobenius angles:  $\pm0.140267993779$, $\pm0.140267993779$
Angle rank:  $1$ (numerical)
Jacobians:  21

This isogeny class is not 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 21 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 27889 1313265121 48533125431184 1771234321111425625 64615351242614110697929 2357222761669014187505971456 85993803755390704220551980623449 3137139833444958204159608891993675625 114445997961845435511963596960277825980944 4175104451049335537166318161729395034795513041

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 142 35996 6965272 1330891188 254196094202 48551250764126 9273284602641782 1771197290588526628 338298681609528711112 64615048178184553182956

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-139}) \)$)$
All geometric endomorphisms are defined over $\F_{191}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.a_ajj$2$(not in LMFDB)
2.191.by_bmt$2$(not in LMFDB)
2.191.z_qs$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.a_ajj$2$(not in LMFDB)
2.191.by_bmt$2$(not in LMFDB)
2.191.z_qs$3$(not in LMFDB)
2.191.a_jj$4$(not in LMFDB)
2.191.az_qs$6$(not in LMFDB)