3.) Given the followingelliptic curvey²x³+ 5x + 4 mod 13.

Part A:

Answer the following to calculate the lower and upper bounds on the number of integer points on this curve:

p = [ Select ] ["4", "5", "13"]

a = [ Select ] ["4", "5", "13"]

b = [ Select ] ["4", "5", "13"]

Using Hasse^'s Theorem,

The lower and upper bounds on the number of integer points on this curve are [ Select ] ["5 #E 15", "7 #E 21", "10 #E 20"]

Part B:

What is the double of the point (1,6) on this curve? [ Select ] ["2P = (10, 1)", "2P = (2, 12)", "2P = (1, 10)"]

Part C:

What is the addition of points (1,6) and (0,2) on this curve? [ Select ] ["P + Q = (3, 2)", "P + Q = (2, 3)", "P + Q = (1, 8)"]

Where it says select choose from the answers in the bracket to the right

Elliptic Curve and Parameters Given elliptic curve: =2+ 5z +4 (mod 13) Parameters: a=>5b b=4 p=13 1. Bounds on the Number of Integer Points Using Hasse's theorem, the number of integer points N on the elliptic curve over a finite field : p+1-2,/p<>