Properties

Label 2.181.abv_biy
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:  $( 1 - 26 x + 181 x^{2} )( 1 - 21 x + 181 x^{2} )$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.214985517670$
Angle rank:  $2$ (numerical)
Jacobians:  30

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 30 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25116 1060497984 35154029239056 1151964785540185344 37738717907375914450476 1236354423520245860113920000 40504199243755138075879429472556 1326958063274723719950672862422979584 43472473121139404984130738220523030069136 1424201691976583259286168053461123475852254784

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 135 32369 5928426 1073309329 194264868075 35161835500118 6364290964549695 1151936657508506689 208500535057942132866 37738596846943203185129

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.av 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.af_ahc$2$(not in LMFDB)
2.181.f_ahc$2$(not in LMFDB)
2.181.bv_biy$2$(not in LMFDB)
2.181.ao_ih$3$(not in LMFDB)
2.181.ac_abl$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.af_ahc$2$(not in LMFDB)
2.181.f_ahc$2$(not in LMFDB)
2.181.bv_biy$2$(not in LMFDB)
2.181.ao_ih$3$(not in LMFDB)
2.181.ac_abl$3$(not in LMFDB)
2.181.abo_bdh$6$(not in LMFDB)
2.181.abc_tp$6$(not in LMFDB)
2.181.c_abl$6$(not in LMFDB)
2.181.o_ih$6$(not in LMFDB)
2.181.bc_tp$6$(not in LMFDB)
2.181.bo_bdh$6$(not in LMFDB)