This formula... is indeed beautiful!
After admiring it for a while, Qiao Yu immediately began to verify it. After all, a formula's aesthetics alone aren't enough; it must also be functional.
What he needed to do was to determine the accuracy of his formula.
Qiao Yu selected the classic elliptic curve y^2=x^3+x.
According to the known conditions of the BSD conjecture, the curve's deficiency is 1. By directly substituting this into the formula and simplifying, the result is: θ=5. Well, 5 to the power of 1 is still 5.
The conclusion is obviously correct.
Because this is a classic Elmert curve, the rational points on the curve were calculated over ten years ago.
Next came the Mordell curve, a special case of the Fermat curve, and various cases of the Kubert curve... Qiao Yu tried them all.
For instance, the Mordell curve: y^2=x^3+k, with k as an integer. He verified cases with known finite rational points, such as k=-1 and k=2, and all proved to be correct.
