ASKSAGE: Sage Q&A Forum - RSS feedhttps://ask.sagemath.org/questions/Q&A Forum for SageenCopyright Sage, 2010. Some rights reserved under creative commons license.Sun, 15 Dec 2013 10:39:33 +0100Finding Cremona label for Tunnell's y^2-x^3-n^2xhttps://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/When I enter
E = EllipticCurve([-n^2,0]); E;E.label()
Sage gives an error that I have an unsupported operand type. I assume the problem is that I have not defined the variable 'n', which is a square free integer, but how does one do this? Any help would be greatly appreciated!!Mon, 02 Jul 2012 11:20:30 +0200https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/Answer by John Cremona for <p>When I enter </p>
<p>E = EllipticCurve([-n^2,0]); E;E.label()</p>
<p>Sage gives an error that I have an unsupported operand type. I assume the problem is that I have not defined the variable 'n', which is a square free integer, but how does one do this? Any help would be greatly appreciated!!</p>
https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?answer=15782#post-id-15782E.label() only works if E is defined over Q and has conductor within the range of the database (currently up to 300,000, but you have to install an optional spkg to get conductors over 10000).
In your case you wanted to treat n as a variable, so your E is (perhaps) defined over the function field Q(n); such a curve does not have a "Cremona label" -- I should know!
Tue, 10 Dec 2013 05:43:44 +0100https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?answer=15782#post-id-15782Comment by John Cremona for <p>E.label() only works if E is defined over Q and has conductor within the range of the database (currently up to 300,000, but you have to install an optional spkg to get conductors over 10000).</p>
<p>In your case you wanted to treat n as a variable, so your E is (perhaps) defined over the function field Q(n); such a curve does not have a "Cremona label" -- I should know!</p>
https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=16536#post-id-16536Personally, I am trying to move towards using LMFDB labels instead since there is at least a logical explanation for the ordering used: see http://www.lmfdb.org/knowledge/show/ec.q.lmfdb_labelSun, 15 Dec 2013 10:39:33 +0100https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=16536#post-id-16536Comment by kcrisman for <p>E.label() only works if E is defined over Q and has conductor within the range of the database (currently up to 300,000, but you have to install an optional spkg to get conductors over 10000).</p>
<p>In your case you wanted to treat n as a variable, so your E is (perhaps) defined over the function field Q(n); such a curve does not have a "Cremona label" -- I should know!</p>
https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=16553#post-id-16553Haha! Though I bet eventually someone will name something after you that you won't have known of!Tue, 10 Dec 2013 13:36:01 +0100https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=16553#post-id-16553Answer by kcrisman for <p>When I enter </p>
<p>E = EllipticCurve([-n^2,0]); E;E.label()</p>
<p>Sage gives an error that I have an unsupported operand type. I assume the problem is that I have not defined the variable 'n', which is a square free integer, but how does one do this? Any help would be greatly appreciated!!</p>
https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?answer=13784#post-id-13784Correct; `n` is indeed a builtin thing in Sage, but it's for numerical approximation.
sage: var('n')
n
sage: E = EllipticCurve([-n^2,0]); E
Elliptic Curve defined by y^2 = x^3 + (-n^2)*x over Symbolic Ring
but there is no `E.label()`, as you'll find if you try it.
Mon, 02 Jul 2012 11:28:33 +0200https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?answer=13784#post-id-13784Comment by memory13 for <p>Correct; <code>n</code> is indeed a builtin thing in Sage, but it's for numerical approximation.</p>
<pre><code>sage: var('n')
n
sage: E = EllipticCurve([-n^2,0]); E
Elliptic Curve defined by y^2 = x^3 + (-n^2)*x over Symbolic Ring
</code></pre>
<p>but there is no <code>E.label()</code>, as you'll find if you try it.</p>
https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=19451#post-id-19451Thank you!Mon, 02 Jul 2012 19:15:31 +0200https://ask.sagemath.org/question/9122/finding-cremona-label-for-tunnells-y2-x3-n2x/?comment=19451#post-id-19451