Properties

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

Learn more about

Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $( 1 - 26 x + 181 x^{2} )( 1 - 20 x + 181 x^{2} )$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.233262291643$
Angle rank:  $2$ (numerical)
Jacobians:  100

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 100 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25272 1061828352 35158284310968 1151969933920665600 37738699782737963730552 1236354297238790133385363200 40504198847814019653163452212472 1326958062593061604562509210936934400 43472473121304776474215552299413346837048 1424201691982291105658430207832510831646752512

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32410 5929144 1073314126 194264774776 35161831908682 6364290902336776 1151936656916753566 208500535058735279464 37738596847094450100730

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.au 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 $\F_{181}$.

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.ag_agc$2$(not in LMFDB)
2.181.g_agc$2$(not in LMFDB)
2.181.bu_bhy$2$(not in LMFDB)
2.181.an_io$3$(not in LMFDB)
2.181.ab_as$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.ag_agc$2$(not in LMFDB)
2.181.g_agc$2$(not in LMFDB)
2.181.bu_bhy$2$(not in LMFDB)
2.181.an_io$3$(not in LMFDB)
2.181.ab_as$3$(not in LMFDB)
2.181.abs_bfy$4$(not in LMFDB)
2.181.ai_aec$4$(not in LMFDB)
2.181.i_aec$4$(not in LMFDB)
2.181.bs_bfy$4$(not in LMFDB)
2.181.abn_bco$6$(not in LMFDB)
2.181.abb_ti$6$(not in LMFDB)
2.181.b_as$6$(not in LMFDB)
2.181.n_io$6$(not in LMFDB)
2.181.bb_ti$6$(not in LMFDB)
2.181.bn_bco$6$(not in LMFDB)
2.181.abl_bbc$12$(not in LMFDB)
2.181.az_su$12$(not in LMFDB)
2.181.al_jc$12$(not in LMFDB)
2.181.ab_u$12$(not in LMFDB)
2.181.b_u$12$(not in LMFDB)
2.181.l_jc$12$(not in LMFDB)
2.181.z_su$12$(not in LMFDB)
2.181.bl_bbc$12$(not in LMFDB)