\\ Pari/GP code for working with elliptic curve 14586.e4


\\ Define the curve: 
E = ellinit([1, 0, 1, 292714, 54762104])

\\ Torsion subgroup: 
elltors(E)

\\ Conductor: 
ellglobalred(E)[1]

\\ Discriminant: 
E.disc

\\ j-invariant: 
E.j

\\ Real Period: 
if(E.disc>0,2,1)*E.omega[1]

\\ Tamagawa numbers: 
gr=ellglobalred(E); [[gr[4][i,1],gr[5][i][4]] | i<-[1..#gr[4][,1]]]

\\ Torsion order: 
elltors(E)[1]

\\ q-expansion of modular form: 
xy = elltaniyama(E);
x*deriv(xy[1])/(2*xy[2]+E.a1*xy[1]+E.a3)

\\ Special L-value: 
ar = ellanalyticrank(E);
ar[2]/factorial(ar[1])

\\ Local data: 
ellglobalred(E)[5]