Properties

Label 2.181.abu_bid
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:  $( 1 - 25 x + 181 x^{2} )( 1 - 21 x + 181 x^{2} )$
Frobenius angles:  $\pm0.120568372405$, $\pm0.214985517670$
Angle rank:  $2$ (numerical)
Jacobians:  54

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 54 curves, and hence is principally polarizable:

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 25277 1062164817 35162381331728 1151996370787078425 37738817740406149256477 1236354696209563650303897600 40504199886318140508072958398677 1326958064519493646406046354462246825 43472473122742273056773508647180261306768 1424201691975694068243198227738783676944777937

Point counts of the curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ 136 32420 5929834 1073338756 194265381976 35161843255382 6364291065513496 1151936658589095556 208500535065629729794 37738596846919641338180

Decomposition and endomorphism algebra

Endomorphism algebra over $\F_{181}$
The isogeny class factors as 1.181.az $\times$ 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 is a list of all twists of this isogeny class.
TwistExtension DegreeCommon base change
2.181.ae_agh$2$(not in LMFDB)
2.181.e_agh$2$(not in LMFDB)
2.181.bu_bid$2$(not in LMFDB)