I put this [MSE question][1] a few days ago, but no one seemed willing to answer it.

So I decided to put it on here and restate the question:

The Elkies curve 
$$
E:y^2+xy+y=x^3−x^2−20067762415575526585033208209338542750930230312178956502x+34481611795030556467032985690390720374855944359319180361266008296291939448732243429
$$
Discriminant of Elkies curve is  $\Delta_E=3581775273581124569703746471783026864293570422220790957452423023734755536293093609524369063657264581131816964723217401534371110750621252297523717205467915359744000000=2^{15}\times 3^6\times 5^6\times 7^4\times 11^2\times 13^4\times 17^5\times 19^3\times 48463\times 20650099\times 315574902691581877528345013999136728634663121\times 376018840263193489397987439236873583997122096511452343225772113000611087671413$

and its conductor
$f=33455601108357547341532253864901605231198511505793733138900595189472144724781456635380154149870961231592352897621963802238155192936274322687070=2\times 3^2\times 5\times 7\times 11\times 13\times 17\times 19\times 48463\times 20650099\times 315574902691581877528345013999136728634663121\times 376018840263193489397987439236873583997122096511452343225772113000611087671413$

We assume the Generalized Riemann Hypothesis (GRH), then $\text{rank}_\mathbb{Z}E(\mathbb{Q})=28$.
If we add the BSD conjecture, can we calculate the order of $Ш(E/\mathbb{Q})$? I thought that under such powerful conditions, it might be easy to add computational tools(such as Magma/SageMath).


[1]: https://math.stackexchange.com/questions/4714027/tate-shafarevich-group-of-elkies-curve