Properties

Label 2.199.acc_brj
Base Field $\F_{199}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

Learn more about

Invariants

Base field:  $\F_{199}$
Dimension:  $2$
L-polynomial:  $( 1 - 27 x + 199 x^{2} )^{2}$
Frobenius angles:  $\pm0.0936959350875$, $\pm0.0936959350875$
Angle rank:  $1$ (numerical)
Jacobians:  3

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 3 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 29929 1542211441 62047696145296 2459278975263398649 97393608417578426434849 3856887397085382882981673216 152736585349876556899743089181409 6048521424971645481410295572923093929 239527496557048975947351895098681903194896 9485528389763576336420173174436926777076824801

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 146 38940 7873472 1568178484 312079380086 62103846717006 12358664488314794 2459374195982737444 489415464197048750528 97393677360918958704300

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abb 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-67}) \)$)$
All geometric endomorphisms are defined over $\F_{199}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.a_amt$2$(not in LMFDB)
2.199.cc_brj$2$(not in LMFDB)
2.199.bb_uk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.a_amt$2$(not in LMFDB)
2.199.cc_brj$2$(not in LMFDB)
2.199.bb_uk$3$(not in LMFDB)
2.199.a_mt$4$(not in LMFDB)
2.199.abb_uk$6$(not in LMFDB)