Properties

Label 2.32.ao_dr
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:  $1 - 14 x + 95 x^{2} - 448 x^{3} + 1024 x^{4}$
Frobenius angles:  $\pm0.0356965878095$, $\pm0.421632723418$
Angle rank:  $2$ (numerical)
Number field:  4.0.12352.2
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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $658$ $1040956$ $1070512702$ $1096393152736$ $1125204363503458$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $19$ $1019$ $32671$ $1045599$ $33533699$ $1073696699$ $34359842543$ $1099511133823$ $35184356292115$ $1125899825493179$

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 4.0.12352.2.

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
2.32.o_dr$2$2.1024.ag_acep