E has torsion Z/3Z and rank exactly 7. It is isomorphic to the Tate form y^2 + 1047xy - 2301807y = x^3 (a1 = 1047, a3 = -2301807), in which (0,0) is a point of order 3. Every curve with a rational point of order 3 has such a form y^2 + a1 xy + a3 y = x^3, and (a1, a3) and (a1/u, a3/u^3) give isomorphic curves (x -> u^2 x, y -> u^3 y), so the curve is determined by t = a3/a1^3: it is the member t = -767269/382576941 (in lowest terms) of the one-parameter Z/3 family y^2 + xy + ty = x^3. The submitted a-invariants are the global minimal model of this curve (the Tate form above is already minimal; the two differ by a translation), on which the point (0,0) of the Tate form is (91351, -1196579).
Rank exactly 7: the seven points listed are independent (regulator 14165.357), and the 2-Selmer group has rank 7 (E has no rational 2-torsion; root number -1), so the rank is at most 7. The Selmer computation assumes GRH for the class groups of the cubic fields involved. Confirmed in PARI/GP (ellrank [7, 7]). It beats the previous T[3] rank-7 records in discriminant (#1661, https://elliptic-rank.icarm.cloud/curve/1661).
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Lewis Combes ·