Properties

Label 2.181.aby_blz
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:  $( 1 - 25 x + 181 x^{2} )^{2}$
Frobenius angles:  $\pm0.120568372405$, $\pm0.120568372405$
Angle rank:  $1$ (numerical)
Jacobians:  16

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 16 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 24649 1056185001 35137532446864 1151928831456275625 37738705586833646899729 1236354709770217963261956096 40504200797827919818896803132569 1326958068552350574450152154977375625 43472473134445293526388455657638204941584 1424201692000467951679894329279996876751092441

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 132 32236 5925642 1073275828 194264804652 35161843641046 6364291208736012 1151936662090031908 208500535121759180322 37738596847576101448156

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.az 2 and its endomorphism algebra is $\mathrm{M}_{2}($\(\Q(\sqrt{-11}) \)$)$
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_akd$2$(not in LMFDB)
2.181.by_blz$2$(not in LMFDB)
2.181.z_rc$3$(not in LMFDB)
Below is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.a_akd$2$(not in LMFDB)
2.181.by_blz$2$(not in LMFDB)
2.181.z_rc$3$(not in LMFDB)
2.181.a_kd$4$(not in LMFDB)
2.181.az_rc$6$(not in LMFDB)