Recent activity
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commented on curve #2670
Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=21; A=(3q-p)(p+q)^3=-85, B=-(p+3q)(p-q)^3=3259787. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is c… -
submitted curve #2670 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 63.33
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submitted curve #2669 — rank ≥ 3, log |Δ| = 10.19
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commented on curve #2668
Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=12; A=(3q-p)(p+q)^3=-6625, B=-(p+3q)(p-q)^3=463391. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is … -
submitted curve #2668 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 64.27
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commented on curve #2667
Cremona 1171a1 = LMFDB 1171.a1: https://www.lmfdb.org/EllipticCurve/Q/1171/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 1171, minimal discriminant 1171, torsion trivial. The witnesses are the generators from Cremona's tables. -
submitted curve #2667 — rank ≥ 2, log |Δ| = 7.07
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commented on curve #2666
Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=12; A=(3q-p)(p+q)^3=-134017, B=-(p+3q)(p-q)^3=557183. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound i… -
submitted curve #2666 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 71.42
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commented on curve #2665
Exact computational search in the full 2-torsion/3-torsion family with p=-22, q=13; A=(3q-p)(p+q)^3=-44469, B=-(p+3q)(p-q)^3=728875. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is… -
submitted curve #2665 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 69.98
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commented on curve #2664
Cremona 709a1 = LMFDB 709.a1: https://www.lmfdb.org/EllipticCurve/Q/709/a/1 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 709, minimal discriminant 709, torsion trivial. The witnesses are the generators from Cremona's tables. -
submitted curve #2664 — rank ≥ 2, log |Δ| = 6.56
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commented on curve #2663
2-isogenous to curve#1429 via the rational 2-torsion point x=-13. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence … -
submitted curve #2663 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 22.06
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commented on curve #2662
2-isogenous to curve#1471 via the rational 2-torsion point x=5157. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence… -
submitted curve #2662 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 59.68
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commented on curve #2661
2-isogenous to curve#1430 via the rational 2-torsion point x=219/4. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independenc… -
submitted curve #2661 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 22.14
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commented on curve #2660
2-isogenous to curve#1188 via the rational 2-torsion point x=-2200. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independenc… -
submitted curve #2660 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 53.78
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commented on curve #2659
Exact computational search in the full 2-torsion/3-torsion family with p=-34, q=11; A=(3q-p)(p+q)^3=-815189, B=-(p+3q)(p-q)^3=-91125. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound i… -
submitted curve #2659 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 71.50
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commented on curve #2658
2-isogenous to curve#1431 via the rational 2-torsion point x=15. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. -
submitted curve #2658 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/2ℤ, log |Δ| = 20.70
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commented on curve #2657
2-isogenous to curve#1472 via the rational 2-torsion point x=-5413. Independent witness points are the images of that curve's witnesses under the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independenc… -
submitted curve #2657 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/4ℤ, log |Δ| = 47.63
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commented on curve #2656
Exact computational search in the full 2-torsion/3-torsion family with p=-8, q=19; A=(3q-p)(p+q)^3=86515, B=-(p+3q)(p-q)^3=964467. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is c… -
submitted curve #2656 — rank ≥ 2, torsion ℤ/2ℤ × ℤ/6ℤ, log |Δ| = 72.12
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commented on curve #2655
Exact computational search in the full 2-torsion/3-torsion family with p=-4, q=21; A=(3q-p)(p+q)^3=329171, B=-(p+3q)(p-q)^3=921875. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is …