Properties

Label 1.463.abh
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:  $1 - 33 x + 463 x^{2}$
Frobenius angles:  $\pm0.221837873022$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-763}) \)
Galois group:  $C_2$
Jacobians:  $4$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $431$ $214207$ $99262748$ $45954470331$ $21276742246421$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $431$ $214207$ $99262748$ $45954470331$ $21276742246421$ $9851127738101104$ $4561072095505175219$ $2111776380476002153683$ $977752464190743595293524$ $452699390921196946268632807$

Jacobians and polarizations

This isogeny class contains the Jacobians of 4 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 \(\Q(\sqrt{-763}) \).

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.bh$2$(not in LMFDB)