Properties

Label 1.199.ar
Base Field $\F_{199}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{199}$
Dimension:  $1$
L-polynomial:  $1 - 17 x + 199 x^{2}$
Frobenius angles:  $\pm0.294151794293$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$
Jacobians:  5

This isogeny class is simple and geometrically simple.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $1$
Slopes:  $[0, 1]$

Point counts

This isogeny class contains the Jacobians of 5 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 183 39711 7885836 1568306523 312079703493 62103828944304 12358664060638827 2459374190157479763 489415464138830696964 97393677360308696184951

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 183 39711 7885836 1568306523 312079703493 62103828944304 12358664060638827 2459374190157479763 489415464138830696964 97393677360308696184951

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{199}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).
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
1.199.r$2$(not in LMFDB)
1.199.al$3$(not in LMFDB)
1.199.bc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.199.r$2$(not in LMFDB)
1.199.al$3$(not in LMFDB)
1.199.bc$3$(not in LMFDB)
1.199.abc$6$(not in LMFDB)
1.199.l$6$(not in LMFDB)