Properties

Label 2.32.an_dv
Base field $\F_{2^{5}}$
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:  $\F_{2^{5}}$
Dimension:  $2$
L-polynomial:  $1 - 13 x + 99 x^{2} - 416 x^{3} + 1024 x^{4}$
Frobenius angles:  $\pm0.198096667756$, $\pm0.390746191731$
Angle rank:  $2$ (numerical)
Number field:  4.0.4152017.1
Galois group:  $D_{4}$
Jacobians:  $15$
Isomorphism classes:  15

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $695$ $1079335$ $1087472060$ $1100797576475$ $1125903767077225$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $20$ $1054$ $33185$ $1049802$ $33554550$ $1073765431$ $34360117280$ $1099513010898$ $35184362257505$ $1125899775560814$

Jacobians and polarizations

This isogeny class contains the Jacobians of 15 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{2^{5}}$.

Endomorphism algebra over $\F_{2^{5}}$
The endomorphism algebra of this simple isogeny class is 4.0.4152017.1.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.32.n_dv$2$2.1024.bd_bnt