Elliptic Curve Rank Leaderboard

This is the Mordell curve E : y² = x³ + 1190790012412, with 1190790012412 = 38038²·823 = 2²·7²·11²·13²·19²·823. It has j(E)=0 and geometric complex multiplication by Z[ζ₃], while End_Q(E)=Z; equivalently, E is a sextic twist of y²=x³+1. The minimal discriminant is Δ = -612567728781193921272945408 = -2⁸·3³·7⁴·11⁴·13⁴·19⁴·823², and the bad primes are 2,3,7,11,13,19,823. Their Kodaira types are respectively I₀*, III, IV, IV, IV, IV, II. The conductor is N = 35280726487742736 = 2⁴·3²·7²·11²·13²·19²·823², and the Tamagawa product is 324. Rational torsion is trivial: #E(F₅)=6 and #E(F₃₁)=43, whose gcd is 1. Six independent rational integral points give rank(E/Q) ≥ 6, while the supplied PARI/GP computation gives the matching upper bound, hence rank(E/Q)=6 and E(Q) ≅ Z⁶. The submitted six-point lattice agrees with the PARI generator lattice via an integral transition matrix of determinant 1. It has been saturated at ℓ=2,3,5,7,11,13. Therefore, if its index i in the full Mordell-Weil group is greater than 1, every prime divisor of i is at least 17. The displayed height determinant 1643.70836038493465... is the regulator of this rank-6 lattice; the global regulator is det(H)/i². A rational 3-isogeny exists to E' : Y² = X³ - 32151330335124, with X = (x³+4B)/x², Y = y(x³-8B)/x³. Its geometric kernel is {O,(0,±38038√823)}, a Galois-stable subgroup defined over Q(√823). Consequently E' also has rank 6 over Q. An exhaustive integral search for -10599 ≤ x ≤ 10¹¹ finds exactly 30 points with y>0 (60 after sign symmetry). Independently, searching combinations of the Mordell-Weil generators with coefficients -5≤n_i≤5 produces exactly the same 30 positive integral points. ΩE​≈0.0408588818808802051405413396566268225117823… so... " i think" it's a real testing ground / candidate for BSD