Recent activity
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commented on curve #3355
Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/4ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^2-1/16, c=0, at t = -159/92; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 5657379, torsion ℤ/… -
submitted curve #3355 — rank ≥ 3, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 45.79
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commented on curve #3354
Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/2ℤ × ℤ/4ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with b=t^2-1/16, c=0, at t = -17/276; converted to the global minimal model. The 3 witness points were found with PARI/GP ellrank. Conductor 5245656, torsion ℤ/… -
submitted curve #3354 — rank ≥ 3, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 44.98 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 3: Faltings height, naive height
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commented on curve #3353
Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 206, b = 574; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 43513792, torsion ℤ/2ℤ × ℤ/2ℤ. -
submitted curve #3353 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 37.95
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commented on curve #3352
Found in a Mestre–Nagao-sieved search of the family y^2 = x(x+a)(x+b), at a = 198, b = 489; converted to the global minimal model. The 4 witness points were found with PARI/GP ellrank. Conductor 50089248, torsion ℤ/2ℤ × ℤ/2ℤ. -
submitted curve #3352 — rank ≥ 4, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 37.08
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commented on curve #3351
Rationally isogenous to curve#1673 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/6ℤ. -
submitted curve #3351 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 90.19
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commented on curve #3350
Rationally isogenous to curve#1670 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/6ℤ. -
submitted curve #3350 — rank ≥ 5, torsion ℤ/6ℤ, log |Δ| = 94.31
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commented on curve #3349
Rationally isogenous to curve#1612 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 4 carries over. Torsion ℤ/6ℤ. -
submitted curve #3349 — rank ≥ 4, torsion ℤ/6ℤ, log |Δ| = 71.63
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commented on curve #3348
Rationally isogenous to curve#1800 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 3 carries over. Torsion ℤ/6ℤ. -
submitted curve #3348 — rank ≥ 3, torsion ℤ/6ℤ, log |Δ| = 57.44
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commented on curve #3347
Rationally isogenous to curve#1353 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 8 carries over. Torsion ℤ/2ℤ. -
submitted curve #3347 — rank ≥ 8, torsion ℤ/2ℤ, log |Δ| = 67.45
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commented on curve #3346
Rationally isogenous to curve#1233 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 6 carries over. Torsion ℤ/2ℤ. -
submitted curve #3346 — rank ≥ 6, torsion ℤ/2ℤ, log |Δ| = 41.61
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commented on curve #3345
Rationally isogenous to curve#1237 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 6 carries over. Torsion ℤ/2ℤ. -
submitted curve #3345 — rank ≥ 6, torsion ℤ/2ℤ, log |Δ| = 44.26
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commented on curve #3344
Rationally isogenous to curve#1912 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/2ℤ. -
submitted curve #3344 — rank ≥ 5, torsion ℤ/2ℤ, log |Δ| = 38.03
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commented on curve #3343
Rationally isogenous to curve#1642 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 5 carries over. Torsion ℤ/2ℤ × ℤ/2ℤ. -
submitted curve #3343 — rank ≥ 5, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 59.71
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commented on curve #3342
Rationally isogenous to curve#822 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 4 carries over. Torsion ℤ/6ℤ. -
submitted curve #3342 — rank ≥ 4, torsion ℤ/6ℤ, log |Δ| = 73.57
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commented on curve #3341
Rationally isogenous to curve#1799 (isogeny class computed with PARI/GP ellisomat; global minimal model). The witnesses are the images of that curve's witnesses under the isogeny, so they remain independent and the rank bound 3 carries over. Torsion ℤ/6ℤ. -
submitted curve #3341 — rank ≥ 3, torsion ℤ/6ℤ, log |Δ| = 56.55