Properties

Label 2.151.abr_bdj
Base field $\F_{151}$
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:  $\F_{151}$
Dimension:  $2$
L-polynomial:  $1 - 43 x + 763 x^{2} - 6493 x^{3} + 22801 x^{4}$
Frobenius angles:  $\pm0.127932556465$, $\pm0.188722117555$
Angle rank:  $2$ (numerical)
Number field:  4.0.435725.2
Galois group:  $D_{4}$
Jacobians:  $8$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $17029$ $512589929$ $11851992849475$ $270298932124668509$ $6162739940459429993584$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $109$ $22479$ $3442393$ $519920019$ $78503515404$ $11853923018403$ $1789940775049459$ $270281039132147859$ $40812436761094376803$ $6162677950289800155454$

Jacobians and polarizations

This isogeny class contains the Jacobians of 8 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{151}$.

Endomorphism algebra over $\F_{151}$
The endomorphism algebra of this simple isogeny class is 4.0.435725.2.

Base change

This is a primitive isogeny class.

Twists

Below is a list of all twists of this isogeny class.

TwistExtension degreeCommon base change
2.151.br_bdj$2$(not in LMFDB)