Elliptic Curve Rank Leaderboard

E has torsion Z/5Z and rank exactly 7. It is isomorphic to the Tate normal form y^2 + (1 - t)xy - ty = x^3 - tx^2 at t = 132965/633888, in which (0,0) is a point of order 5. Every curve with a rational point P of order 5 can be put in this form (P moved to (0,0) and its tangent to y = 0); t is determined by (E, P), and P -> 2P replaces t by -1/t. The submitted a-invariants are the global minimal model of this curve, on which the point (0,0) of the Tate normal form is (-7184651646, -26713595432910657). It was found by a screen of the discriminant region of this family: all t = a/b with |Delta_min| <= 4.93 x 10^76 (the T[5] rank-8 discriminant record, #1917, https://elliptic-rank.icarm.cloud/curve/1917), most of them in the cusp where |a| is small against b, outside the boxes searched before. A Mestre-Nagao screen in C over 3.4 x 10^13 parameters left 335,529 new candidates for Magma (2-Selmer rank, 2-descent with point search, RankBounds). The family and kind of search are those of hdeping's Mestre-Nagao sieve over the Tate normal form (#1254, https://elliptic-rank.icarm.cloud/curve/1254) and David Renshaw's rational-parameter searches (#1185, https://elliptic-rank.icarm.cloud/curve/1185), carried to the whole region below a discriminant bound. Search scoped and carried out by Claude code Opus 5.5