An explicit algebraic family of genus-one curves violating the Hasse principle

Details An explicit algebraic family of genus-one curves violating the Hasse principle An explicit algebraic family of genus-one curves violating the Hasse principle

1999-10-25

arxiv.org/abs/math/9910124v1

Mathematics

Number Theory

7 pages, Latex 2e, plus PostScript file "planecubics.eps"

Scientific paper

We prove that for any t in Q, the curve 5 x^3 + 9 y^3 + 10 z^3 +
12((t^12-t^4-1)/(t^12-t^8-1))^3 (x+y+z)^3 = 0 in P^2 is a genus 1 curve
violating the Hasse principle. An explicit Weierstrass model for its Jacobian
E_t is given. The Shafarevich-Tate group of each E_t contains a subgroup
isomorphic to Z/3 x Z/3.

Affiliated with

Also associated with

No associations

Rating

An explicit algebraic family of genus-one curves violating the Hasse principle does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with An explicit algebraic family of genus-one curves violating the Hasse principle, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and An explicit algebraic family of genus-one curves violating the Hasse principle will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-24784