Properties

Label 2.181.abu_bih
Base Field $\F_{181}$
Dimension $2$
Ordinary Yes
$p$-rank $2$
Principally polarizable Yes
Contains a Jacobian Yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $( 1 - 23 x + 181 x^{2} )^{2}$
Frobenius angles:  $\pm0.173686936480$, $\pm0.173686936480$
Angle rank:  $1$ (numerical)
Jacobians:  40

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 40 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25281 1062434025 35165659044096 1152017443113770025 37738910498109592648041 1236354998014026605269094400 40504200587794120866520568758641 1326958065320149748922401858967398025 43472473120455939405124729965125417431296 1424201691957191884541184602876158683016265625

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32428 5930386 1073358388 194265859456 35161851838678 6364291175734096 1151936659284147748 208500535054664128906 37738596846429369169948

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.ax 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-195}) \)$)$
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
2.181.a_agl$2$(not in LMFDB)
2.181.bu_bih$2$(not in LMFDB)
2.181.x_nk$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_agl$2$(not in LMFDB)
2.181.bu_bih$2$(not in LMFDB)
2.181.x_nk$3$(not in LMFDB)
2.181.a_gl$4$(not in LMFDB)
2.181.ax_nk$6$(not in LMFDB)