Timeline for Isotropic ternary forms

4 events

when toggle format	what		by	license	comment
Jun 3, 2015 at 19:05	comment	added	user148455		@Will Jagy, Thanks a lot for your answer. I have tried to prove the formula in Cassel's book but I have failed. I am also trying to locate the conference proceedings edited by Olga Taussky you mentioned. Of course, a specific example (apart the trivial ones when one of the positive coefficients is a square) would be very interesting and helpful.
Jun 3, 2015 at 2:50	comment	added	grghxy		@user148455: It is classical via projection from a rational point (as Daniel Loughran suggests) to build a birational isomorphism between a conic with a rational point and the projective line, so composing one such with the inverse of another gives the desired isomorphism between conics. Since you have rational points in your case of interest, that is what you should do. If all you have is passage of congruence tests, then follow Gauss; look at the table of contents and flip the pages of an actual copy of the book and you'll find what is needed spread over many sections.
Jun 2, 2015 at 10:59	comment	added	user148455		Thank you for your comments. But I still do not know how to obtain $M$ even for the the example. All I have is the congruence conditions from the fact that $f$ is isotropic. @grghxy, could you please be more specific about your reference to Gauss' Disquisitiones?
Jun 2, 2015 at 0:33	history	answered	grghxy	CC BY-SA 3.0