Recent activity
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submitted curve #3798 — rank ≥ 6, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 123.77 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 6: Faltings height, naive height
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commented on curve #3797
(u,v) = (13547,6956) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3797 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 105.34
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commented on curve #3796
(u,v) = (22165,7076) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3796 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 109.75
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commented on curve #3795
(u,v) = (18236,473) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3795 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 97.58
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commented on curve #3794
(u,v) = (33189,212) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3794 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 99.16
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commented on curve #3793
(u,v) = (21024,527) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3793 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 99.15
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commented on curve #3792
Specialization at T = 167565/784 of the rank-16 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 5834T^2 - 3278T - 340636, p = -68221T - 15735, q = 7870T^2 + 129138T - 767092, D = 34(3842980T^3 - 457913811T^2 - 1358784043T + 3024… -
commented on curve #3771
Specialization at T = 1969/15181 of the rank-16 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 28139T^2 + 30542T - 534071, p = 3500T^2 + 607734T - 29070, q = 3807T^2 + 8441T - 3536, D = -12(6076000T^4 - 261217124T^3 - 139665348… -
commented on curve #3768
Specialization at T = 18065/427 of the rank-16 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 26893T^2 - 4132T + 249889, p = 802T + 75146, q = 95524T^2 - 98001T - 52965, D = -6(9660432T^3 - 491890783T^2 + 697221412T + 666719787… -
commented on curve #3762
Specialization at T = 1547/3050 of the rank-16 fibration of X1008 given by: y^2 + (Lx+B)y = x(x+D)(x+E), where B = pE + qD + pq(L-p-q), L = 66118T^2 + 260158T - 72323, p = -3001T - 11, q = 204774T^2 + 267483T - 2147712, D = -264840140T^3 - 585787782T^2 + 5921807000T - 7146… -
recorded the primes of bad reduction of curve #3792 — rank ≥ 30, log |Δ| = 367.89
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recorded the primes of bad reduction of curve #3790 — rank ≥ 28, log |Δ| = 323.24
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recorded the primes of bad reduction of curve #3789 — rank ≥ 28, log |Δ| = 323.88
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submitted curve #3792 — rank ≥ 30, log |Δ| = 367.89
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submitted curve #3791 — rank ≥ 28, log |Δ| = 354.15
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submitted curve #3790 — rank ≥ 28, log |Δ| = 323.24
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submitted curve #3789 — rank ≥ 28, log |Δ| = 323.88
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submitted curve #3788 — rank ≥ 9, torsion ℤ/3ℤ, log |Δ| = 115.85
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submitted curve #3787 — rank ≥ 9, torsion ℤ/3ℤ, log |Δ| = 108.47 ☆ record for ℤ/3ℤ torsion, rank ≥ 9: naive height
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submitted curve #3786 — rank ≥ 7, torsion ℤ/3ℤ, log |Δ| = 74.60 ☆ record for ℤ/3ℤ torsion, rank ≥ 7: naive height
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submitted curve #3785 — rank ≥ 4, torsion ℤ/3ℤ, log |Δ| = 32.38 ☆ record for ℤ/3ℤ torsion, rank ≥ 4: naive height
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commented on curve #3784
(u,v) = (8008,5311) for the C2 x C4 family y^2 = x(x+u^2)(x+v^2). PARI/GP gives exact rank 5. -
submitted curve #3784 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 99.51
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recorded the primes of bad reduction of curve #3773 — rank ≥ 30, log |Δ| = 399.62
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recorded the primes of bad reduction of curve #3772 — rank ≥ 30, log |Δ| = 397.50