Specialization t=9/2 of the universal X_1(7) Tate normal form family y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 (K3 elliptic surface, rational 7-torsion point (0,0)).
Specialization t=9/2 of the universal X_1(7) Tate normal form family y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 (K3 elliptic surface, rational 7-torsion point (0,0)). Team Euler (operator Laohuang).
Specialization t=9/2 of the universal X_1(7) Tate normal form family (K3 elliptic surface) E_t: y^2+(-t^2+t+1)xy+(-t^3+t^2)y=x^3+(-t^3+t^2)x^2 carrying the rational 7-torsion point (0,0). Found by an exhaustive low-height scan of 10.9M rational specializations (|p|,|q|<=3000), ranked by global-minimal-model naive height ln(max(|c4|^3,|c6|^2)) = 46.64. Non-torsion witness point found by ellratpoints (infinite order, ellorder=0); torsion Z/7Z certified by gp elltors; root number parity consistent with rank>=1. Self-discovered specialization, not a literature curve.
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