Mestre ten-root construction, roots 0,2,6,13,23,30,39,56,59,70: with p(x) = prod (x - a_i), write p = q^2 - r with q a monic quintic and deg r <= 4; the genus-one curve y^2 = r(x) carries the ten points (a_i, q(a_i)), and this the curve submitted is itsthe minimal Weierstrass model of its Jacobian. Found by enumerating all integer ten-root sets 0 = a_1 < ... < a_10 = R with 64 < R <= 80 (about 1.0e11 sets up to reflection and scaling) and scoring each by the sum of -a_p log(p)/p over 5 <= p <= 199 (with early abort on low partial sums); the sets scoring at least 31 were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.
Mestre ten-root construction, roots 0,2,6,13,23,30,39,56,59,70: with p(x) = prod (x - a_i), write p = q^2 - r with q a monic quintic and deg r <= 4; the curve y^2 = r(x) carries the ten points (a_i, q(a_i)), and this is its minimal Weierstrass model. Found by enumerating all integer ten-root sets 0 = a_1 < ... < a_10 = R with 64 < R <= 80 (about 1.0e11 sets up to reflection and scaling) and scoring each by the sum of -a_p log(p)/p over 5 <= p <= 199 (with early abort on low partial sums); the sets scoring at least 31 were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.
Michael Rubinstein ·
thisthe curve submitted isitsthe minimal Weierstrass model of its Jacobian. Found by enumeratingallinteger ten-root sets 0 = a_1 < ... < a_10= R with 64 < R <= 80 (about 1.0e11 sets up to reflection and scaling)and scoring each by the sum of -a_p log(p)/p over 5 <= p <= 199 (with early abort on low partial sums); the sets scoring at least 31 were screened by exact conductor and by a GRH explicit-formula upper bound on the rank, and the survivors were certified with ellrank. Rank 16, proved: 16 independent points listed, matching the 2-descent upper bound. Torsion trivial.Michael Rubinstein ·