Function: ellanalyticrank
Section: elliptic_curves
C-Name: ellanalyticrank
Prototype: GDGp
Help: ellanalyticrank(e, {eps}): returns the order of vanishing at s=1
 of the L-function of the elliptic curve e and the value of the first
 non-zero derivative. To determine this order, it is assumed that any
 value less than eps is zero. If no value of eps is given, a value of
 half the current precision is used.
Doc: returns the order of vanishing at $s=1$ of the $L$-function of the
 elliptic curve $e$ and the value of the first non-zero derivative. To
 determine this order, it is assumed that any value less than \kbd{eps} is
 zero. If no value of \kbd{eps} is given, a value of half the current
 precision is used.
 \bprog
 ? e = ellinit("11a1"); \\ rank 0
 ? ellanalyticrank(e)
 %2 = [0, 0.2538418608559106843377589233]
 ? e = ellinit("37a1"); \\ rank 1
 ? ellanalyticrank(e)
 %4 = [1, 0.3059997738340523018204836835]
 ? e = ellinit("389a1"); \\ rank 2
 ? ellanalyticrank(e)
 %6 = [2, 1.518633000576853540460385214]
 ? e = ellinit("5077a1"); \\ rank 3
 ? ellanalyticrank(e)
 %8 = [3, 10.39109940071580413875185035]
 @eprog