ASKSAGE: Sage Q&A Forum - Individual question feedhttp://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Fri, 03 Jun 2016 09:50:03 -0500Finding Cremona label of the elliptic curve $y^2 = x^3 - x^2 - 1008x + 48512$http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-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.Fri, 03 Jun 2016 01:59:08 -0500http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-48512/Answer by B r u n o for <p>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. </p>
<p>1) E=EllipticCurve(QQ,[0, -1, 0, -1008, 48512]);E.cremona_label()</p>
<p>2) d=CremonaDatabase().data_from_coefficients([0, -1, 0, -1008, 48512])
d['cremona_label']</p>
<p>I would like to know why I am getting errors and also how to find out the Cremona label of the above elliptic curve.</p>
http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-48512/?answer=33660#post-id-33660You 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'
Fri, 03 Jun 2016 09:50:03 -0500http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-48512/?answer=33660#post-id-33660Answer by slelievre for <p>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. </p>
<p>1) E=EllipticCurve(QQ,[0, -1, 0, -1008, 48512]);E.cremona_label()</p>
<p>2) d=CremonaDatabase().data_from_coefficients([0, -1, 0, -1008, 48512])
d['cremona_label']</p>
<p>I would like to know why I am getting errors and also how to find out the Cremona label of the above elliptic curve.</p>
http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-48512/?answer=33656#post-id-33656Try querying the LMFDB (L-functions and modular forms database)
http://lmfdb.orgFri, 03 Jun 2016 06:40:18 -0500http://ask.sagemath.org/question/33655/finding-cremona-label-of-the-elliptic-curve-y2-x3-x2-1008x-48512/?answer=33656#post-id-33656