# Finding Cremona label for Tunnell's y^2-x^3-n^2x

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!!

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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).

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!

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Haha! Though I bet eventually someone will name something after you that you won't have known of!

( 2013-12-10 13:36:01 +0200 )edit

Personally, 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_label

( 2013-12-15 10:39:33 +0200 )edit

Correct; 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.

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Thank you!

( 2012-07-02 19:15:31 +0200 )edit