Recent activity
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commented on curve #3608
Specialization at T = 3 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #724 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank). -
submitted curve #3608 — rank ≥ 17, log |Δ| = 161.59
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commented on curve #3607
Specialization at T = 5/18 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank). -
submitted curve #3607 — rank ≥ 17, log |Δ| = 172.56
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commented on curve #3606
Specialization at T = 4/5 of the rank-17 fibration of X1008, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #751 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank). -
submitted curve #3606 — rank ≥ 17, log |Δ| = 152.58
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commented on curve #3605
Specialization at T = -3/2 of the rank-17 fibration of X1092, y^2 + (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #1958 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank). -
submitted curve #3605 — rank ≥ 17, log |Δ| = 175.87
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commented on curve #3604
Specialization at t = -2 of a rank-17 elliptic K3 family (member P = 2G + theta of C546 in https://gist.github.com/7fff-zip/58764130a98380def8d555e30ba81344, in reduced coordinates y^2 = x^3 - 27*c4(t)*x - 54*c6(t), c4 = 229266544691230630042225 + 1148767151849671983980280*t + 16… -
submitted curve #3604 — rank ≥ 17, log |Δ| = 155.18
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commented on curve #3603
Specialization at T = 85/531 of the rank-11 fibration of X163, y^2 - (Lx+B)y = x(x+D)(x+E), given in the commentary of curve #718 (same T), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank). -
submitted curve #3603 — rank ≥ 16, log |Δ| = 166.12
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recorded the primes of bad reduction of curve #3602 — rank ≥ 28, log |Δ| = 320.81
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submitted curve #3602 — rank ≥ 28, log |Δ| = 320.81
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submitted curve #3601 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 91.35
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submitted curve #3600 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 77.64
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submitted curve #3599 — rank ≥ 5, torsion ℤ/8ℤ, log |Δ| = 206.79
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commented on curve #3598
It is the fiber at t = 35033/156392 of Elkies' Z/4Z fibration E1 of the singular K3 surface of discriminant −163. The fiber also lies on the rank-5 subfamily, found by Dujella-Peral, defined by the condition 199664t² + 104728t − 122161 = □, parametrized by t = (−u² − 330u + 94936… -
submitted curve #3598 — rank ≥ 11, torsion ℤ/4ℤ, log |Δ| = 210.93 ☆ record for ℤ/4ℤ torsion, rank ≥ 11: conductor
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submitted curve #3597 — rank ≥ 4, torsion ℤ/4ℤ, log |Δ| = 46.46
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submitted curve #3596 — rank ≥ 4, torsion ℤ/4ℤ, log |Δ| = 47.22
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submitted curve #3595 — rank ≥ 4, torsion ℤ/4ℤ, log |Δ| = 47.07
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commented on curve #3594
Specialization at T = 8 of the rank-17 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 46550T^2 + 1624T + 75424, p = -73708T^2 - 57738T + 135450, q = 71955T^2 + 77817T + 8760, D = 12(282127352T^4 + 191775362T^3 - 452929497T^2 + … -
submitted curve #3594 — rank ≥ 19, log |Δ| = 169.60
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submitted curve #3593 — rank ≥ 31, log |Δ| = 487.16
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submitted curve #3592 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 71.24
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recorded the primes of bad reduction of curve #3587 — rank ≥ 31, log |Δ| = 465.76
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submitted curve #3591 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 71.92
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submitted curve #3590 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 77.34
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commented on curve #3589
Specialization at T = 8 of the rank-17 fibration of X1008 given by: y^2 - (Lx+B)y = x(x+D)(x+E), where B = pq(L+p+q) - pE - qD, L = 94992T^2 + 43200T - 74684, p = 45650T^2 - 3480T + 2996, q = 7132T^2 - 71704T - 112100, D = 5(101326060T^4 + 455923735T^3 - 335745592T^2 - 107…