elliptic_curves_order_counter

python

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

        
class EC:
    def __init__(self, a1, a2, a3,a4,a6, p):
        self.a1 = a1
        self.a2 = a2
        self.a3 = a3
        self.a4 = a4
        self.a6 = a6
        self.p = p
        self.calc_order()
    
    def calc_order(self):
        self.points = []
        for x in range(self.p):
            for y in range(self.p):
                pt = Point(x, y)
                if self.oncurve(pt):
                    self.points.append(pt)
        self.points_count = len(self.points)
        self.order = len(self.points) + 1

    def oncurve(self,  pt):
        l = ((pt.y**2) + (self.a1 * pt.x * pt.y) + self.a3 * (pt.y)) % self.p
        r = ((pt.x**3) + self.a2 * (pt.x**2) + self.a4 * pt.x + self.a6) % self.p
        return l == r
    
ec = EC(0, 0, 0, 1, 1,5)

print("F" + str(ec.p))
print( "#EC:" + str(ec.order))