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

asked 2016-06-03 01:59:08 -0500

Suman gravatar image

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.

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answered 2016-06-03 09:50:03 -0500

B r u n o gravatar image

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'
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answered 2016-06-03 06:40:18 -0500

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

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Asked: 2016-06-03 01:59:08 -0500

Seen: 81 times

Last updated: Jun 03 '16