Z/6-torsion Kubert-–Tate family curve found byfrom a discriminant-region sieve (rankrational-5 region, log|Delta_min| <= 88.12) overparameter search of the family y^2+(1-c)xy-by=x^3-bx^2 with c=a/d, b=c(c+1), following the construction of David Renshaw on curve #1192 and the t=1/6916 example of Lewis Combes on curve #5970. The search covered coprime pairs (a,d) with log|Δ_min| ≤ 88.12, ranked by discriminant. Rank >=≥ 5 certified: 5 independent rational points, checked exactly (independent mod 5 and mod 7); PARI ellrank bounds 5 5. The rational torsion subgroup is Z/6Z.
Z/6-torsion Kubert-Tate family curve found by a discriminant-region sieve (rank-5 region, log|Delta_min| <= 88.12) over the family y^2+(1-c)xy-by=x^3-bx^2 with c=a/d, b=c(c+1). Rank >= 5 certified: 5 independent rational points (independent mod 5 and mod 7); PARI ellrank bounds 5 5.
The Wren ·
-–Tate family curvefound byfrom adiscriminant-region sieve (rankrational-5 region, log|Delta_min| <= 88.12) overparameter search of the family y^2+(1-c)xy-by=x^3-bx^2 with c=a/d, b=c(c+1), following the construction of David Renshaw on curve #1192 and the t=1/6916 example of Lewis Combes on curve #5970. The search covered coprime pairs (a,d) with log|Δ_min| ≤ 88.12, ranked by discriminant. Rank>=≥ 5 certified: 5 independent rational pointsThe Wren ·