Properties

Label 2.181.abu_bhs
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:  $1 - 46 x + 876 x^{2} - 8326 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.0160657258716$, $\pm0.248310478721$
Angle rank:  $2$ (numerical)
Number field:  4.0.2376000.1
Galois group:  $D_{4}$
Jacobians:  8

This isogeny class is simple and geometrically 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
$A(\F_{q^r})$ 25266 1061424660 35153368060626 1151938068205665360 37738555284740103399666 1236353786555283316251291060 40504197362480181857744905499346 1326958058893234075220347881986012160 43472473112963795676652186169674459878306 1424201691963442899882804236471069814325912500

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32398 5928316 1073284438 194264030956 35161817384878 6364290668951176 1151936653704921118 208500535018730678056 37738596846595009015198

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.2376000.1.
All geometric endomorphisms are defined over $\F_{181}$.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.bu_bhs$2$(not in LMFDB)