Recent activity
New submissions and commentary edits, newest first.
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commented on curve #78
Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [1,-1,0,-201814,34925104], |Delta|=643509175703572, I=109. The submitted integral points give the rank >= 8 witness checked by the s… -
submitted curve #78 — rank ≥ 8, naive height 48.26
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submitted curve #79 — rank ≥ 9, naive height 51.07
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commented on curve #77
Provenance: Elkies-Watkins, Elliptic curves of large rank and small conductor (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [1,-1,0,-222751,40537273], |Delta|=584492602941116, I=101. The submitted integral points give the rank >= 8 witness checked by the s… -
submitted curve #77 — rank ≥ 8, naive height 48.56
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commented on curve #76
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (ANTS VI / arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [0,0,1,-23737,960366], |Delta|=457532830151317; their I-column records 96 integral x-coordinates. The submitted integral… -
submitted curve #76 — rank ≥ 8, naive height 41.84
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commented on curve #75
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (ANTS VI / arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [0,1,1,-23846,1022562], |Delta|=409086620841461; their I-column records 78 integral x-coordinates. The submitted integra… -
submitted curve #75 — rank ≥ 8, naive height 41.85
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commented on curve #73
Provenance: Maksym Voznyy (2023), as listed on Andrej Dujella’s high-rank elliptic-curve tables for torsion group Z/2Z. Dujella’s page lists this curve y^2 + xy = x^3 - 131092767138360259739530662694875901594863*x + 11513825206543517171066572416002846205241167788788151682092217 a… -
commented on curve #74
Provenance: Nagao-Kouya (1994), “An example of elliptic curve over Q with rank >= 21,” as reproduced in Nagao, “Construction of high-rank elliptic curves.” The paper gives this minimal model y^2 + xy + y = x^3 + x^2 - 215843772422443922015169952702159835*x - 194743612777871519472… -
submitted curve #74 — rank ≥ 21, naive height 255.69
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submitted curve #73 — rank ≥ 18, naive height 295.64
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commented on curve #72
Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=336, c6=-31320, Delta=-545723 with 545723 prime. The submitted points (-4,0), (-3,5), (-2,6), and (-1,6) were checked exactly on the curve, with an additional finite-fie… -
submitted curve #72 — rank ≥ 4, naive height 20.70
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commented on curve #70
Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=273, c6=999, Delta=11197. The submitted points (0,0), (-1,2), (-2,1) were checked exactly on the curve, with an additional finite-field independence sanity check; the si… -
commented on curve #71
Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=3616, c6=137440, Delta=16430032 = 2^4*353*2909. The submitted points (-2,2), (-6,8), (10,4), (30,154) were checked exactly on the curve, with an additional finite-field … -
commented on curve #69
Provenance: found by a local bounded-height search over reduced integral Weierstrass models. Invariants are c4=1, c6=-865, Delta=-433. The submitted points (0,1), (-1,1) were checked exactly on the curve, with an additional finite-field independence sanity check; the site Neron-T… -
submitted curve #71 — rank ≥ 4, naive height 24.58
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submitted curve #69 — rank ≥ 2, naive height 13.53
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submitted curve #70 — rank ≥ 3, naive height 16.83
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commented on curve #68
Provenance: Noam D. Elkies, "j = 0, rank 15; also 3-rank 6 and 7 in real and imaginary quadratic fields", NMBRTHRY posting, December 30, 2009. This is the Mordell curve y^2 = x^3 + 46974552981863676115647417. The submitted witnesses consist of integral points on this curve plus t… -
submitted curve #68 — rank ≥ 15, naive height 131.75
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commented on curve #67
Provenance: Andrej Dujella rank-record table "Rank >= 27", Elkies (2016). The page lists this curve y^2 + xy = x^3 - 55671146865244401916117773020296610079754015500970*x + 161981895322788558220906653027519611838007321625214218991719656790551905956 and the 27 independent points su… -
commented on curve #66
Provenance: Andrej Dujella rank-record table "Rank >= 26", Elkies (2006). The page lists this curve y^2 + xy = x^3 - 271568164801421919805097494520335727505515190*x + 1673523352045742769296938739782713519216640490554763586630258973092 and the 26 independent points submitted here. -
commented on curve #65
Provenance: Andrej Dujella rank-record table "Rank >= 25", Elkies (2006). The page lists this curve y^2 + xy = x^3 - 1222583105876029916237789137035775062690200*x + 523967447200209449943328506898413682821590945806099349816040000 and the 25 independent points submitted here. -
commented on curve #64
Provenance: Noam D. Elkies, "Rank of an elliptic curve and 3-rank of a quadratic field via the Burgess bounds", ANTS XVI. This is the minimal model (7) for E_{16D}, y^2 + y = x^3 + (D-1)/4 with D = 72513834653847828539450325493. The submitted points are the 16 independent points … -
submitted curve #67 — rank ≥ 27, naive height 355.27
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submitted curve #66 — rank ≥ 26, naive height 318.55
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submitted curve #65 — rank ≥ 25, naive height 302.36