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on Exact rank of the Elkies-Klagsbrun elliptic curve

The statement

Let $E$ be the elliptic curve over $\mathbb{Q}$ defined by the Weierstrass equation

y^2 + xy = x^3 - 27006183241630922218434652145297453784768054621836357954737385\,x + 55258058551342376475736699591118191821521067032535079608372404779149413277716173425636721497.

Assuming the generalized Riemann hypothesis, prove that the rank of $E(\mathbb{Q})$ equals exactly $29$ .

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