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math.NT2007★ 1 cited
Tate-Shafarevich groups and K3 surfaces
Patrick Corn
Following (and elaborating on) a method of Logan and van Luijk, we exhibit explicit genus-2 curves whose Jacobians have nontrivial 2-torsion in their Tate-Shafarevich groups.
math.NT2005★ 1 cited
Note on the rank of quadratic twists of Mordell equations
Sungkon Chang
14H52 : Elliptic curves Let E be the elliptic curve given by a Mordell equation y^2=x^3-A where A is an integer. For certain A, we use Stoll's formula to compute a lower bound for…
math.NT2005★ 1 cited
Galois Groups Via Atkin-Lehner Twists
Pete L. Clark
Using Serre's proposed complement to Shih's Theorem, we obtain PSL_2(F_p) as a Galois group over Q for at least 614 new primes p. Under the assumption that rational elliptic curves…