Properties

Label 1.367.ah
Base field $\F_{367}$
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:  $\F_{367}$
Dimension:  $1$
L-polynomial:  $1 - 7 x + 367 x^{2}$
Frobenius angles:  $\pm0.441516776861$
Angle rank:  $1$ (numerical)
Number field:  \(\Q(\sqrt{-1419}) \)
Galois group:  $C_2$
Jacobians:  $12$

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

$r$ $1$ $2$ $3$ $4$ $5$
$A(\F_{q^r})$ $361$ $135375$ $49438228$ $18140926875$ $6657789405091$

Point counts of the curve

$r$ $1$ $2$ $3$ $4$ $5$ $6$ $7$ $8$ $9$ $10$
$C(\F_{q^r})$ $361$ $135375$ $49438228$ $18140926875$ $6657789405091$ $2443410261558000$ $896731551429079573$ $329100478703723641875$ $120779875684915849764796$ $44326214376614826497964375$

Jacobians and polarizations

This isogeny class contains the Jacobians of 12 curves (of which all are hyperelliptic), and hence is principally polarizable:

Decomposition and endomorphism algebra

All geometric endomorphisms are defined over $\F_{367}$.

Endomorphism algebra over $\F_{367}$
The endomorphism algebra of this simple isogeny class is \(\Q(\sqrt{-1419}) \).

Base change

This is a primitive isogeny class.

Twists

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

TwistExtension degreeCommon base change
1.367.h$2$(not in LMFDB)