On the conjecture of Birch and Swinnerton-Dyer for an elliptic curve of rank $3$

Abstract:

The elliptic curve ${y^2} = 4{x^3} - 28x + 25$ has rank 3 over Q. Assuming the Weil-Taniyama conjecture for this curve, we show that its L-series $L(s)$ has a triple zero at $s = 1$ and compute ${\lim _{s \to 1}}L(s)/{(s - 1)^3}$ to 28 decimal places; its value agrees with the product of the regulator and real period, in accordance with the Birch-Swinnerton-Dyer conjecture if III is trivial.