Properties

Label 1.463.as
Base field $\F_{463}$
Dimension $1$
$p$-rank $1$
Ordinary yes
Supersingular no
Simple yes
Geometrically simple yes
Primitive yes
Principally polarizable yes
Contains a Jacobian yes

Related objects

Downloads

Learn more

Invariants

Base field:  $\F_{463}$
Dimension:  $1$
L-polynomial:  $1 - 18 x + 463 x^{2}$
Frobenius angles:  $\pm0.362638179038$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-382}) \)
Galois group:  $C_2$
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:  $1$
Slopes:  $[0, 1]$

Point counts

Point counts of the abelian variety

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $446$ $214972$ $99272018$ $45954134496$ $21276725876846$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $446$ $214972$ $99272018$ $45954134496$ $21276725876846$ $9851127468622204$ $4561072096726232834$ $2111776380633341858688$ $977752464194057836831454$ $452699390921213416991236732$

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 $\F_{463}$.

Endomorphism algebra over $\F_{463}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-382}) \).

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
1.463.s$2$(not in LMFDB)