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Is there an elliptic curve mod n with exactly one point?

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up vote 3 down vote favorite 1 I have tried many elliptic curves $y^2 = x^3 + ax +b$ with no success. I know that for prime modules there exists a minimum number of points the elliptic curve has to have, and I couldn't satisfy this for the smallest primes. So I decided to try luck with modules with few quadratic residues such as 8. But again, no luck. elliptic-curves share | cite | improve this question asked Nov 16 at 18:04 SlowerPhoton 408 1 11 1 ...