Properties

Label 2.199.abz_boc
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:  $( 1 - 28 x + 199 x^{2} )( 1 - 23 x + 199 x^{2} )$
Frobenius angles:  $\pm0.0391815390403$, $\pm0.196619630811$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 30444 1547894736 62074910607696 2459362031800974144 97393740848463325045524 3856887120251138490827202816 152736582016542676442671475773764 6048521408058651258062035736304555264 239527496492990168787393881473421384473296 9485528389563662810027362232356287439827162576

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 149 39085 7876928 1568231449 312079804439 62103842259406 12358664218598441 2459374189105787089 489415464066160350272 97393677358866325188325

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The isogeny class factors as 1.199.abc $\times$ 1.199.ax 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 are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.af_ajm$2$(not in LMFDB)
2.199.f_ajm$2$(not in LMFDB)
2.199.bz_boc$2$(not in LMFDB)
2.199.am_fp$3$(not in LMFDB)
2.199.ag_h$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.199.af_ajm$2$(not in LMFDB)
2.199.f_ajm$2$(not in LMFDB)
2.199.bz_boc$2$(not in LMFDB)
2.199.am_fp$3$(not in LMFDB)
2.199.ag_h$3$(not in LMFDB)
2.199.abo_bej$6$(not in LMFDB)
2.199.abi_zb$6$(not in LMFDB)
2.199.g_h$6$(not in LMFDB)
2.199.m_fp$6$(not in LMFDB)
2.199.bi_zb$6$(not in LMFDB)
2.199.bo_bej$6$(not in LMFDB)