What CASes say about the analytic rank of rank 8 elliptic curve '457532830151317a1'

Did you read the Sage's documentation on analytic_rank()?

   Return an integer that is *probably* the analytic rank of this
   elliptic curve.  If leading_coefficient is "True" (only implemented
   for PARI), return a tuple (rank, lead) where lead is the value of
   the first non-zero derivative of the L-function of the elliptic
   curve.

So Sage says that it is probably 4. This does not qualify as a bug. Further on, the documentation says:

   Note: It is an open problem to *prove* that *any* particular elliptic
   curve has analytic rank >= 4.

So either the latter is nonsense (well, I am not a number theorist, I don't know), or Magma just solved an open problem for you... Or maybe it didn't, and it fact no CAS can actually compute it.

EDIT: please see this discussion. Also, slide 22 of the talk by J.Cremona explains that there is currently no way to check for sure that the analytic rank $\geq 4$.

According to Magma V2.17-5, the analytic rank is $8$, as it should be. Below $s$ is an approximation of $\frac{L^{(8)}(1)}{8!}$.

E:= EllipticCurve([0,0,1,-23737,960366]);

time r, s :=AnalyticRank(E);

Time: 361.950

r;

8

s;

5087.2