Properties

Label 2.199.abx_bmk
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian No

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Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $( 1 - 25 x + 199 x^{2} )( 1 - 24 x + 199 x^{2} )$
Frobenius angles:  $\pm0.153403448314$, $\pm0.176204172288$
Angle rank:  $2$ (numerical)
Jacobians:  0

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 is principally polarizable, but does not contain a Jacobian.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30800 1552320000 62102311409600 2459492113478400000 97394261343569930894000 3856888928577249780526080000 152736587480732574011743191772400 6048521422068557165964317229542400000 239527496521047881536737561768902184267200 9485528389593307823767194346008346791768000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 151 39197 7880404 1568314393 312081472261 62103871377182 12358664660732779 2459374194802319953 489415464123489378076 97393677359170708537877

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.az $\times$ 1.199.ay 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 $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.ab_ahu$2$(not in LMFDB)
2.199.b_ahu$2$(not in LMFDB)
2.199.bx_bmk$2$(not in LMFDB)