Recent activity
-
commented on curve #4174
Specialization at T = 1/9 of the K3 elliptic fibration y^2 + (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3593; points from PARI ellrank. -
submitted curve #4174 — rank ≥ 16, log |Δ| = 141.11
-
commented on curve #4173
Mestre construction: sextuple [-650, -481, 74, 225, 256, 576], T = 23; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x) = prod(x - a_i), on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by a discriminant-first sweep + Nagao-sum rescoring + ratpoints search on the quartic. -
submitted curve #4173 — rank ≥ 16, log |Δ| = 135.52
-
commented on curve #4172
Mestre construction: sextuple [-494, -490, -156, 308, 342, 490], T = 413; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x)=prod(x-a_i) on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by Nagao-sum sieve + ratpoints search on the quartic. -
submitted curve #4172 — rank ≥ 16, log |Δ| = 133.07
-
commented on curve #4171
Specialization at T = 2748/203 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -8601190111439927121627T^8 + 70553802194275661608968T^7 - 40117514965744884873804T^6 - 394125757357369375667736T^5 - 727539205447352323463130T^4 - 33716394035501269… -
submitted curve #4171 — rank ≥ 25, log |Δ| = 278.63
-
commented on curve #4170
Specialization at T = -1163/397 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -8601190111439927121627T^8 + 70553802194275661608968T^7 - 40117514965744884873804T^6 - 394125757357369375667736T^5 - 727539205447352323463130T^4 - 3371639403550126… -
submitted curve #4170 — rank ≥ 27, log |Δ| = 303.30
-
submitted curve #4169 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 76.42 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 7: naive height
-
submitted curve #4168 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 74.89 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 7: discriminant, Faltings height
-
submitted curve #4167 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 75.86
-
submitted curve #4166 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 78.51
-
submitted curve #4165 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 81.32 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 7: conductor
-
submitted curve #4164 — rank ≥ 7, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 84.79
-
submitted curve #4163 — rank ≥ 8, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 87.18 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 8: discriminant, Faltings height, naive height
-
commented on curve #4162
Mestre construction: sextuple [-345, -264, 33, 69, 195, 312], T = 271; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x), p(x)=prod(x-a_i) on the locus sum a_i = 0, 12 p5 = 5 p2 p3. Found by Nagao-sum sieve + ratpoints search on the quartic. -
submitted curve #4162 — rank ≥ 17, log |Δ| = 134.45
-
submitted curve #4161 — rank ≥ 9, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 112.77 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9: naive height
-
submitted curve #4160 — rank ≥ 9, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 107.33 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9: discriminant, Faltings height
-
submitted curve #4159 — rank ≥ 9, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 123.05 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 9: conductor
-
submitted curve #4158 — rank ≥ 10, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 126.54 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 10: conductor, discriminant, Faltings height, naive height
-
improved curve #4157 from rank ≥ 9 to rank ≥ 10 — torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 127.49
-
submitted curve #4157 — rank ≥ 10, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 127.49
-
commented on curve #4156
Mestre construction: sextuple [-311, -241, -196, -123, 427, 444], T = 13; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x). -
submitted curve #4156 — rank ≥ 16, log |Δ| = 123.17
-
commented on curve #4155
Mestre construction: sextuple [-291, -162, -97, -42, 259, 333], T = 4; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x). -
submitted curve #4155 — rank ≥ 16, log |Δ| = 125.96
-
commented on curve #4154
Mestre construction: sextuple [-1024, -624, -616, -341, 1240, 1365], T = 368; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x).