Timeline for Is the rank of the elliptic curve x^3 + y^3 = a(n), where a(n) is the n-th cubefree taxicab number, known?
Current License: CC BY-SA 3.0
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| Feb 10, 2016 at 11:25 | comment | added | Kimball | I think the answer to this question is simply: no. | |
| S Feb 10, 2016 at 3:35 | history | suggested | Tadashi |
Added relevant tag
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| Feb 10, 2016 at 3:01 | review | Suggested edits | |||
| S Feb 10, 2016 at 3:35 | |||||
| Oct 25, 2013 at 20:07 | comment | added | Jonathan Sondow | In Unsolved Problems in Number Theory, 3rd edition, section D1, 2004, R. K. Guy says, "Andrew Bremner has computed the rational rank of the elliptic curve x^3 + y^3 = Taxicab(n) as equal to 2, 4, 5, 4 for n = 2, 3, 4, 5, respectively." But Taxicab(n) equals A011541(n), not the cubefree taxicab number A080642(n). @Lucia | |
| Oct 22, 2013 at 22:26 | comment | added | Lucia | For partial results towards this see Silverman's paper maa.org/sites/default/files/images/upload_library/22/Ford/… . In particular it says that the rank of the elliptic curve is bounded below in terms of the number of solutions to the taxicab equation (see page 339). I am not aware of a more precise solution. | |
| Oct 22, 2013 at 22:00 | history | asked | Jonathan Sondow | CC BY-SA 3.0 |