Question

Elliptic curve y^2 = x^3 + 7x +11

Compute the order of the elliptic curve over the finite field F127

Answer 1

@Zarkon please helpp

Answer 2

@wio or @Miracrown any ideas?

Answer 3

This problem is a bit rusty on me. I'm working on it though!

Answer 4

@Miracrown awesome thank you soo much!

Answer 5

@AccessDenied any ideas?

Answer 6

i am able to use mathematica if that helps at all

Answer 7

What class is this?

Answer 8

abstract alg

Answer 9

Sorry, I am viewing out of interest to see how it is approached. I don't think I know enough to be of help here, although I'll try some research in the mean time. :)

Answer 10

thank youuu

Answer 11

so unfortunately, p = 127 is prime
so the methods of Hasse are not of much use
generally when you are considering elliptic curve over its prime fields, the primes are usually small and thus allowing you to compute it by hand

I'm trying to think of a different way besides counting
otherwise, you'd have to check 127 cases

Answer 12

In what context did this question come?
That might help lead me to an approach

Answer 13

Is this from an algorithms section? Theoretical section? computational section? @cbrezovs

Answer 14

we are studying elliptic curve cryptography

Answer 15

and we are supposed to use the program mathematica to help us

Answer 16

are u familiar with mathematica?

Answer 17

how would i go about doing it if i checked all 127 cases?

Answer 18

@Miracrown ?