Properties

Label 2.191.abw_bkw
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:  $( 1 - 24 x + 191 x^{2} )^{2}$
Frobenius angles:  $\pm0.165219579186$, $\pm0.165219579186$
Angle rank:  $1$ (numerical)
Jacobians:  105

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 105 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28224 1316818944 48550236840000 1771291317720121344 64615486195582895006784 2357222925268823977290240000 85993803337883348580090475788864 3137139829710017809760575045657165824 114445997945963658832753447197055217640000 4175104450999330185526910143441559679133814784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 144 36094 6967728 1330934014 254196625104 48551254133758 9273284557619184 1771197288479817214 338298681562582691088 64615048177410656806654

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.ay 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-47}) \)$)$
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_ahm$2$(not in LMFDB)
2.191.bw_bkw$2$(not in LMFDB)
2.191.y_ov$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.191.a_ahm$2$(not in LMFDB)
2.191.bw_bkw$2$(not in LMFDB)
2.191.y_ov$3$(not in LMFDB)
2.191.a_hm$4$(not in LMFDB)
2.191.ay_ov$6$(not in LMFDB)