Properties

Label 2.181.aby_bly
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:  $( 1 - 26 x + 181 x^{2} )( 1 - 24 x + 181 x^{2} )$
Frobenius angles:  $\pm0.0828936782352$, $\pm0.149335043618$
Angle rank:  $2$ (numerical)
Jacobians:  8

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 8 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24648 1056117504 35136641521800 1151922333134536704 37738671201839627609928 1236354562792731291567840000 40504200264537239477794303173768 1326958066874666182738394385306353664 43472473129869101358024477738575424112200 1424201691989956968566809907815194727332797184

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 132 32234 5925492 1073269774 194264627652 35161839461018 6364291124941812 1151936660633628574 208500535099811072772 37738596847297580676554

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.aba $\times$ 1.181.ay 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.ac_akc$2$(not in LMFDB)
2.181.c_akc$2$(not in LMFDB)
2.181.by_bly$2$(not in LMFDB)
2.181.ar_hm$3$(not in LMFDB)
2.181.af_adq$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.ac_akc$2$(not in LMFDB)
2.181.c_akc$2$(not in LMFDB)
2.181.by_bly$2$(not in LMFDB)
2.181.ar_hm$3$(not in LMFDB)
2.181.af_adq$3$(not in LMFDB)
2.181.abr_bfm$6$(not in LMFDB)
2.181.abf_uk$6$(not in LMFDB)
2.181.f_adq$6$(not in LMFDB)
2.181.r_hm$6$(not in LMFDB)
2.181.bf_uk$6$(not in LMFDB)
2.181.br_bfm$6$(not in LMFDB)