$p$-adic regulator calculations

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I was thinking I should add an answer of my own since it's too long for a comment. I did some digging into the github library files and got the following comment:

# when gens() calls mwrank it passes the command-line
# parameter "-p 100" which helps curves with large
# coefficients and 2-torsion and is otherwise harmless.
# This is pending a more intelligent handling of mwrank
# options in gens() (which is nontrivial since gens() needs
# to parse the output from mwrank and this is seriously
# affected by what parameters the user passes!).
# In fact it would be much better to avoid the mwrank console at
# all for gens() and just use the library. This is in
# progress (see trac #1949).

on lines 1907-1916 of this. So in effect, there is currently no code yet for taking the generators directly from the Cremona Database.

I have very limited knowledge in programming and coding but based on my experimentation so far, this is what I got on SAGE in terms of trying to get the code from the generators in the database:

D = CremonaDatabase()
x = EllipticCurve();
N = x.conductor();
y = str(N);
z = len(y);
a = x.cremona_label()[z:]; a
P = D.allgens(N)[a]; P
R0 = P[0]; R0
# R1 = P[1]; R1
Q0 = x(R0)
# Q1 = x(R1)
h = x.padic_height(p, prec)
h(Q0)
# h(Q1)

Then essentially P are the generators that we need, except that they are in the form of a nested list, ie. [[a,b,c],[d,e,f],...] as opposed to when using E.gens() and getting output as [(a : b : c),(d : e : f),...]

With this workaround, I can now obtain padic heights -> the padic height matrix and the discriminant -> padic regulator. Of course this hasn't been written into a proper code yet but it is a workaround.