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May 7, 2012 at 21:45 comment added Francesco Polizzi You are right, $6$ is the lowest possible degree, as it also mentioned in Mella-Polastri's paper. I added this in the answer.
May 7, 2012 at 21:40 history edited Francesco Polizzi CC BY-SA 3.0
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May 7, 2012 at 17:52 comment added user5117 Historical comment: another example of birational plane curves that are not Cremona equivalent comes from the 10-nodal plane sextic. If I understand correctly, this is the lowest-degree rational plane curve that cannot be transformed into a line by Cremona transformations. This was known already to Coble before 1920, and presumably to others much earlier.
May 7, 2012 at 17:03 history edited Francesco Polizzi CC BY-SA 3.0
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May 7, 2012 at 9:25 vote accept Maarten Derickx
May 7, 2012 at 9:20 history edited Francesco Polizzi CC BY-SA 3.0
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May 7, 2012 at 9:08 history answered Francesco Polizzi CC BY-SA 3.0