Recent activity
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commented on curve #3741
(u,v) = (199,4) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 3. -
submitted curve #3741 — rank ≥ 3, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 42.35
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commented on curve #3740
(u, v)=(29716, 3025) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3740 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 108.89
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commented on curve #3737
(u, v) = (266, 143) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 4. -
submitted curve #3739 — rank ≥ 29, log |Δ| = 354.16
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submitted curve #3738 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 74.41
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submitted curve #3737 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 66.61 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 4: naive height
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submitted curve #3736 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 85.43
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submitted curve #3735 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 75.98
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recorded the primes of bad reduction of curve #3733 — rank ≥ 28, log |Δ| = 332.24
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recorded the primes of bad reduction of curve #3732 — rank ≥ 28, log |Δ| = 332.32
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commented on curve #3734
Found 2026-09-30 in a direct search of the full rational 2-torsion family y^2 = x(x+da)(x+db), using the primitive smooth additive relation 2096 + 2449 = 4545 and twist d = -95. Candidates were screened with Mestre–Nagao sums and then checked with PARI/GP 2.17.4. PARI/GP ellrank … -
submitted curve #3734 — rank ≥ 6, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 69.52
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submitted curve #3733 — rank ≥ 28, log |Δ| = 332.24
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submitted curve #3732 — rank ≥ 28, log |Δ| = 332.32
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submitted curve #3731 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 79.94
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submitted curve #3730 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 77.30
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submitted curve #3729 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 78.61
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submitted curve #3728 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 80.86
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commented on curve #3727
Specialization at T = -8/9 of a rank-17 fibration of X1008 (2-neighbour of the one in curve#751). -
submitted curve #3727 — rank ≥ 18, log |Δ| = 163.01 ★ record for rank ≥ 18: conductor
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commented on curve #3726
Specialization at T = -3/2 of a rank-17 fibration of X1092 (two 2-neighbour steps from the one in curve#1879). -
submitted curve #3726 — rank ≥ 19, log |Δ| = 176.91 ★ record for rank ≥ 19: conductor
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commented on curve #3725
Found 2026-09-30 in a direct search of the full rational 2-torsion family y^2 = x(x+da)(x+db), using the primitive smooth additive relation 71 + 2545 = 2616 and twist d = 145. Candidates were screened by a deep Mestre–Nagao sieve and then checked with PARI/GP 2.17.4. The submitte… -
submitted curve #3725 — rank ≥ 6, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 72.58
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commented on curve #3724
Found 2026-09-30 in a direct search of the full rational 2-torsion family y^2 = x(x+da)(x+db), using the primitive smooth additive relation 2169 + 3776 = 5945 and twist d = -5. Candidates were screened by a deep Mestre–Nagao sieve and then checked with PARI/GP 2.17.4. The submitt… -
submitted curve #3724 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 53.33 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 5: conductor
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commented on curve #3723
Specialization at T = -8899/5648 of the rank-9 fibration of X400 (equations as in curve#802). -
submitted curve #3723 — rank ≥ 18, torsion ℤ/2ℤ, log |Δ| = 281.68 ☆ record for ℤ/2ℤ torsion, rank ≥ 18: discriminant, Faltings height, naive height