Properties

Label 2.199.acb_bqi
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:  $( 1 - 27 x + 199 x^{2} )( 1 - 26 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0936959350875$, $\pm0.126927281034$
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
$A(\F_{q^r})$ 30102 1544292804 62059590469656 2459329592340224160 97393786012966189230402 3856887923923467324839727936 152736586638371737259817904612962 6048521427229326783669064148522547840 239527496557492143221170658064709901481336 9485528389744280111620696896397238091954053604

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 147 38993 7874982 1568210761 312079949157 62103855200186 12358664592573243 2459374196900727601 489415464197954253738 97393677360720832652153

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abb $\times$ 1.199.aba 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_als$2$(not in LMFDB)
2.199.b_als$2$(not in LMFDB)
2.199.cb_bqi$2$(not in LMFDB)