Recent activity
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submitted curve #4190 — rank ≥ 26, log |Δ| = 272.64
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commented on curve #4189
Specialization at T = -609/8 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -159593418515992752T^8 + 66594122607180400704T^7 - 9577916877180584429856T^6 + 378921666915696440595168T^5 - 8319401481873790592668080T^4 + 11627268030949343240070892… -
submitted curve #4189 — rank ≥ 24, log |Δ| = 266.70
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recorded the primes of bad reduction of curve #4188 — rank ≥ 26, log |Δ| = 280.38
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commented on curve #4188
Specialization at T = -257/517 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -113946597679617331526187T^8 - 628704898397157619416528T^7 - 910139814353468861642484T^6 + 13879376823678260295456T^5 - 533762798296920925528530T^4 + 16390037876010… -
submitted curve #4188 — rank ≥ 26, log |Δ| = 280.38
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commented on curve #4187
Specialization at T = 1815/788 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -28627871103769984370352T^8 + 250727503810391437739328T^7 - 288854657346414564166464T^6 - 1046563569239575640345856T^5 - 2237723908977579748622280T^4 - 292953908312… -
submitted curve #4187 — rank ≥ 25, log |Δ| = 258.15 ★ record for rank ≥ 25: conductor
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recorded the primes of bad reduction of curve #4185 — rank ≥ 16, log |Δ| = 109.47
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submitted curve #4186 — rank ≥ 17, log |Δ| = 120.73 ★ record for rank ≥ 17: discriminant, Faltings height, naive height
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submitted curve #4185 — rank ≥ 16, log |Δ| = 109.47
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commented on curve #4184
Independently constructed eight-point plane cubic pencil 1005a6f72cab52f0 at t=-114/1709. Rank exactly 16: exact local 2-descent characters certify 16 independent rational points, and unconditional PARI algebraic 2-descent gives upper bound 16. The displayed quadratic base change… -
submitted curve #4184 — rank ≥ 16, log |Δ| = 103.86 ★ record for rank ≥ 16: discriminant, Faltings height, naive height
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submitted curve #4183 — rank ≥ 18, log |Δ| = 134.82 ★ record for rank ≥ 18: discriminant, Faltings height, naive height
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submitted curve #4182 — rank ≥ 17, log |Δ| = 124.31
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submitted curve #4181 — rank ≥ 16, log |Δ| = 106.95
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commented on curve #4180
Specialization at T = -29/96 of a rank-17 fibration of X1152 not posted before: y^2 = x^3 + A4 x + A6, where A4 = -6490299971789709696747T^8 - 122171843220159373604496T^7 - 507701052166171299717636T^6 + 1050551383991494297232448T^5 - 1535498496547466925264930T^4 + 218246535030425… -
submitted curve #4180 — rank ≥ 23, log |Δ| = 227.54
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commented on curve #4179
Mestre construction: sextuple [-1053, -495, 8, 39, 456, 1045], T = 153; 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 #4179 — rank ≥ 17, log |Δ| = 140.71
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commented on curve #4178
Mestre construction: sextuple [-1524, -1034, 94, 254, 780, 1430], T = 149; 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 #4178 — rank ≥ 17, log |Δ| = 140.50
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commented on curve #4177
Mestre construction: sextuple [-803, -792, 315, 365, 427, 488], T = 517; 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 #4177 — rank ≥ 17, log |Δ| = 136.95
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commented on curve #4176
Specialization at T = 3 of the K3 elliptic fibration y^2 - (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3589; points from PARI ellrank. -
submitted curve #4176 — rank ≥ 17, log |Δ| = 136.88
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commented on curve #4175
Specialization at T = 7 of the K3 elliptic fibration y^2 + (Lx+B)y = x(x+D)(x+E) given in the commentary of database curve #3857; points from PARI ellrank. -
submitted curve #4175 — rank ≥ 16, log |Δ| = 142.66
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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