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- W4300107857 abstract "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." @default.
- W4300107857 created "2022-10-03" @default.
- W4300107857 creator A5034540754 @default.
- W4300107857 date "1999-10-25" @default.
- W4300107857 modified "2023-09-29" @default.
- W4300107857 title "An explicit algebraic family of genus-one curves violating the Hasse principle" @default.
- W4300107857 doi "https://doi.org/10.48550/arxiv.math/9910124" @default.
- W4300107857 hasPublicationYear "1999" @default.
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