Properties

Label 2.181.abv_bjd
Base field $\F_{181}$
Dimension $2$
$p$-rank $2$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

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Invariants

Base field:  $\F_{181}$
Dimension:  $2$
L-polynomial:  $1 - 47 x + 913 x^{2} - 8507 x^{3} + 32761 x^{4}$
Frobenius angles:  $\pm0.132251908937$, $\pm0.187299602773$
Angle rank:  $2$ (numerical)
Number field:  4.0.657725.1
Galois group:  $D_{4}$
Jacobians:  $13$

This isogeny class is simple and geometrically simple, primitive, ordinary, and not supersingular. It is principally polarizable and contains a Jacobian.

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $2$
Slopes:  $[0, 0, 1, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $25121$ $1060834709$ $35158215653501$ $1151992660939088309$ $37738847788163620114176$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $135$ $32379$ $5929131$ $1073335299$ $194265536650$ $35161848751323$ $6364291171661775$ $1151936659945323459$ $208500535074017267211$ $37738596846803275495654$

Jacobians and polarizations

This isogeny class contains the Jacobians of 13 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{181}$.

Endomorphism algebra over $\F_{181}$
The endomorphism algebra of this simple isogeny class is 4.0.657725.1.

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.bv_bjd$2$(not in LMFDB)