Recent activity
New submissions and commentary edits, newest first.
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submitted curve #64 — rank ≥ 16, naive height 143.66
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commented on curve #63
Provenance: Elkies, 2009, as listed on Andrej Dujella’s high-rank elliptic-curve tables for torsion group Z/2Z. Dujella’s rank-18 page lists this curve and the 18 independent points submitted here. -
commented on curve #62
Provenance: Noam D. Elkies, Mordell curves with large rank, and Elkies, ANTS XVI, section 4.2. This is the lower-height member E_k: y^2 = x^3 + k with k = -908800736629952526116772283648363 from a 3-isogenous rank-17 pair. The submitted rational points are dual-3-isogeny images o… -
commented on curve #61
Provenance: Noam D. Elkies, 2009 rank-13 Mordell curve y^2 = x^3 + 48163745551486811536. Andrew Sutherland’s MIT rank-record page lists this curve with the 13 independent integral points submitted here. -
submitted curve #63 — rank ≥ 18, naive height 303.36
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submitted curve #62 — rank ≥ 17, naive height 165.30
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submitted curve #61 — rank ≥ 13, naive height 95.85
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commented on curve #59
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=9: [0,0,1,-167419,30261330], |Delta|=95276302704064331; their I-column records 135 integral x-coordinates. The submitted points certi… -
commented on curve #60
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=10: [1,-1,0,-1536664,648294124], |Delta|=50881111474471687972; their I-column records 207 integral x-coordinates. Also appears in Tab… -
commented on curve #58
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=8: [0,1,1,-16440,1394010], |Delta|=561715239383323; their I-column records 84 integral x-coordinates. The submitted points certify ra… -
commented on curve #56
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=6: [0,0,1,-277,4566], |Delta|=7647224363; their I-column records 49 integral x-coordinates. The submitted points certify rank >= 6 he… -
commented on curve #57
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=7: [0,0,1,-1387,68046], |Delta|=1829517077483; their I-column records 71 integral x-coordinates. The submitted points certify rank >=… -
commented on curve #55
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=5: [1,0,0,-22,219], |Delta|=20384311; their I-column records 29 integral x-coordinates. The submitted points certify rank >= 5 here. -
commented on curve #55
Provenance: Elkies-Watkins, "Elliptic curves of large rank and small conductor" (arXiv:math/0403374), Table 4 low absolute-discriminant list for r=5: [1,0,0,-22,219], |Delta|=20384311; their I-column records 29 integral x-coordinates. The submitted points certify rank >= 5 here. -
submitted curve #60 — rank ≥ 10, naive height 54.35
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submitted curve #59 — rank ≥ 9, naive height 47.97
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submitted curve #57 — rank ≥ 7, naive height 35.78
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submitted curve #58 — rank ≥ 8, naive height 41.83
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submitted curve #56 — rank ≥ 6, naive height 30.38
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submitted curve #55 — rank ≥ 5, naive height 24.32
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commented on curve #54
Smallest conductor of an elliptic curve of rank 4: conductor 234446 = 2·117223, Cremona label 234446a1 / LMFDB 234446.a1, y^2 + x·y = x^3 − x^2 − 79x + 289. By completeness of Cremona's tables below conductor 500000, this is the provably minimal conductor in rank 4. Generators [6… -
commented on curve #53
Smallest conductor of an elliptic curve of rank 3: conductor 5077 (prime), Cremona label 5077a1 / LMFDB 5077.a1, y^2 + y = x^3 − 7x + 6. Cremona's tables are complete below conductor 500000, so 5077 is the provably minimal conductor in rank 3. Generators [1,0], [2,0], [0,2]. -
submitted curve #54 — rank ≥ 4, naive height 24.73
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submitted curve #53 — rank ≥ 3, naive height 17.45
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submitted curve #52 — rank ≥ 13, naive height 201.24
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submitted curve #51 — rank ≥ 13, naive height 190.91
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commented on curve #50
Smallest known conductor of an elliptic curve with rank ≥ 11 (Elkies–Watkins, 2004). From their paper "Elliptic Curves of Large Rank and Small Conductor" (arXiv:math/0403374). -
commented on curve #49
Smallest known conductor of an elliptic curve with rank ≥ 10 (Elkies–Watkins, 2004). From their paper "Elliptic Curves of Large Rank and Small Conductor" (arXiv:math/0403374). -
commented on curve #48
Smallest known conductor of an elliptic curve with rank ≥ 9 (Elkies–Watkins, 2004). From their paper "Elliptic Curves of Large Rank and Small Conductor" (arXiv:math/0403374). -
submitted curve #50 — rank ≥ 11, naive height 61.51