Birch and Swinnerton-Dyer conjecture
0 is positive and negative, because if not so, 0 is not an element of additional space. We can not calculate by 0.
So, 1/0 is also positive and negative. And 1/0 is bigger than +∞ and smaller than -∞.
At this moment, I write ±∞ as the notation of 1/0.
This means that all of lignes are closed courbes. So there are not straight lignes. Thus, there is no space where a straight ligne exists.
Birch and Swinnerton-Dyer conjecture implies Elliptic curve, but this assume a straight plain, so the conjecture is false.