how to use magma to find the rank of the elliptic curve

Question

I am trying to find as much as possible of elliptic curves in Magma. What is the code for finding the rank of elliptic curve in Magma? I want to write a for loop for the curve $y^2=y^3+ax^2+bx+c$ for ($-30 <a,b<30$). Could someone help me with the code?

Answer 1

You can simply use the following code:

${\tt P<x>:=PolynomialRing(RationalField());\\ for \,\,a \,\,in\,\, [-30..30]\,\, do\\ for \,\,b \,\,in\,\, [-30..30]\,\, do\\ for \,\,c \,\,in\,\, [-30..30]\,\, do\\ if \,\,Discriminant(x^3+a*x^2+b*x+c) \,\,ne\,\, 0 \,\,then\\ E:=EllipticCurve([0,a,0,b,c]);\\ print\,\, E,Rank(E);\\ end\,\, if;\\ end\,\, for;\\ end\,\, for;\\ end\,\, for;}$