Ask Your Question

# Finding Cremona label of the elliptic curve $y^2 = x^3 - x^2 - 1008x + 48512$

I want to find out the Cremona label of the elliptic curve given by $$y^2 = x^3 - x^2 - 1008x + 48512.$$ I have tried the following commands in Sage but getting errors.

1) E=EllipticCurve(QQ,[0, -1, 0, -1008, 48512]);E.cremona_label()

2) d=CremonaDatabase().data_from_coefficients([0, -1, 0, -1008, 48512]) d['cremona_label']

I would like to know why I am getting errors and also how to find out the Cremona label of the above elliptic curve.

edit retag close merge delete

## 2 answers

Sort by ยป oldest newest most voted

You need to install the optional package database_cremona_ellcurve which contains many more curves than the default database included into Sage:

sage -i database_cremona_ellcurve


Then your first try works:

sage: E = EllipticCurve(QQ,[0, -1, 0, -1008, 48512])
sage: E.cremona_label()
'48400ch1'

more

Try querying the LMFDB (L-functions and modular forms database) http://lmfdb.org

more

## Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

## Stats

Asked: 2016-06-03 01:59:08 -0600

Seen: 210 times

Last updated: Jun 03 '16