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m = 239; n = 48
X = 2*m*n; Y = m^2 - n^2; Z = m^2 + n^2
E = EllipticCurve([0, 2*(Z^2-X*Y), 0, (X*Y)^2, 0])
E
Elliptic Curve defined by y^2 = x^3 + 4547218754*x^2 + 1581862737670677504*x over Rational Field 
N = E.conductor()
N
factor(N)
952876293752470080 2^6 * 3 * 5 * 7 * 41 * 191 * 239 * 2377 * 31873 
%time E.mwrank()
Mwrank crashed -- automatically restarting.
Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/sage/schemes/elliptic_curves/ell_rational_field.py", line 465, in mwrank return mwrank(list(self.a_invariants())) File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/sage/interfaces/mwrank.py", line 271, in __call__ raise ValueError(err) ValueError: Invalid input ([0, 4547218754, 0, 1581862737670677504, 0]) to mwrank (singular curve)
CPU time: 0.05 s, Wall time: 12.63 s 
2^63
9223372036854775808 
float(log(1581862737670677504,2))
60.45633012682668 
2^62
4611686018427387904 
E.discriminant()
574515608492206198067952082088767978288273998206730240000 
mw = E.mwrank_curve()

mw.two_descent()
Error in lines 1-1 Traceback (most recent call last): File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/smc_sagews/sage_server.py", line 905, in execute exec compile(block+'\n', '', 'single') in namespace, locals File "", line 1, in <module> File "/projects/sage/sage-6.9/local/lib/python2.7/site-packages/sage/libs/mwrank/interface.py", line 434, in two_descent second_descent) File "sage/libs/mwrank/mwrank.pyx", line 1070, in sage.libs.mwrank.mwrank._two_descent.do_descent (/projects/sage/sage-6.9/src/build/cythonized/sage/libs/mwrank/mwrank.c:4858) sig_on() File "sage/libs/ntl/error.pyx", line 42, in sage.libs.ntl.error.NTL_error_callback (/projects/sage/sage-6.9/src/build/cythonized/sage/libs/ntl/error.cpp:756) raise NTLError(s) NTLError: RR: division by zero 
%time E.analytic_rank_upper_bound()
1 CPU time: 0.17 s, Wall time: 7.42 s 
%time E.root_number()
-1 CPU time: 0.00 s, Wall time: 0.00 s 
L = E.lseries()