Properties

Label 2.191.abx_blo
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:  $( 1 - 27 x + 191 x^{2} )( 1 - 22 x + 191 x^{2} )$
Frobenius angles:  $\pm0.0686610702072$, $\pm0.206981219725$
Angle rank:  $2$ (numerical)
Jacobians:  20

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 20 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 28050 1314591300 48535526377800 1771217396022016800 64615181813507270343750 2357221878293440716592372800 85993800366218579990782673420550 3137139823211727664318087893031324800 114445997938145246023844393902971130045800 4175104451015671298245531435900684002152062500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 143 36033 6965618 1330878473 254195427673 48551232569418 9273284237164783 1771197284810948593 338298681539471714798 64615048177663556296473

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{191}$
The isogeny class factors as 1.191.abb $\times$ 1.191.aw and its endomorphism algebra is a direct product of the endomorphism algebras for each isotypic factor. The endomorphism algebra for each factor is:
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.af_aie$2$(not in LMFDB)
2.191.f_aie$2$(not in LMFDB)
2.191.bx_blo$2$(not in LMFDB)