Properties

Label 1.181.h
Base Field $\F_{181}$
Dimension $1$
Ordinary Yes
$p$-rank $1$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $1$
L-polynomial:  $1 + 7 x + 181 x^{2}$
Frobenius angles:  $\pm0.583772988431$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-3}) \)
Galois group:  $C_2$
Jacobians:  10

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 10 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 189 33075 5926284 1073250675 194265097929 35161828228800 6364290773491749 1151936658917259075 208500535086218801244 37738596846616577926875

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 189 33075 5926284 1073250675 194265097929 35161828228800 6364290773491749 1151936658917259075 208500535086218801244 37738596846616577926875

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-3}) \).
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below are some of the twists of this isogeny class.
TwistExtension DegreeCommon base change
1.181.ah$2$(not in LMFDB)
1.181.aba$3$(not in LMFDB)
1.181.t$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
1.181.ah$2$(not in LMFDB)
1.181.aba$3$(not in LMFDB)
1.181.t$3$(not in LMFDB)
1.181.at$6$(not in LMFDB)
1.181.ba$6$(not in LMFDB)