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2026-05-28 18:40:50 · David Renshaw

submitted curve #49 — rank ≥ 10, naive height 61.48
2026-05-28 18:27:55 · David Renshaw

submitted curve #48 — rank ≥ 9, naive height 50.31
2026-05-28 16:25:57 · David Renshaw

commented on curve #47

Smallest known conductor of an elliptic curve with rank ≥ 8 (Elkies–Watkins, 2004). From their paper "Elliptic Curves of Large Rank and Small Conductor" (arXiv:math/0403374).
2026-05-28 16:24:30 · David Renshaw

submitted curve #47 — rank ≥ 8, naive height 46.34
2026-05-28 05:22:40 · David Renshaw

commented on curve #46

Rank 16 Mordell curve from 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 (8) for E_{-432D}, with D = 72513834653847828539450325493 = 41 * 1768630113508483622913422573: y^2 + y = x^3 - 489468…
2026-05-28 05:22:23 · David Renshaw

submitted curve #46 — rank ≥ 16, naive height 150.25
2026-05-28 05:19:16 · David Renshaw

commented on curve #45

Rank 13 curve due to Eroshkin (2007), listed on Dujella's high-rank elliptic curves with prescribed torsion page for torsion group Z/3Z: https://web.math.pmf.unizg.hr/~duje/tors/z3old8910111213.html. The model is y^2 + x*y = x^3 - 560715933702165990261993692150795879540*x + 52994…
2026-05-28 05:18:56 · David Renshaw

submitted curve #45 — rank ≥ 13, naive height 279.35
2026-05-28 05:02:16 · David Renshaw

commented on curve #43

Lowest-conductor rank 6 curve in the Sage/Watkins elliptic-curves database: [1, 1, 0, -2582, 48720], conductor 5187563742. The submitted integral points were found by an exact search and certified independent by the site verifier.
2026-05-28 05:02:16 · David Renshaw

commented on curve #44

Lowest-conductor rank 7 curve in the Sage/Watkins elliptic-curves database: [0, 0, 0, -10012, 346900], conductor 382623908456. The submitted integral points were found by an exact search and certified independent by the site verifier.
2026-05-28 05:01:41 · David Renshaw

submitted curve #44 — rank ≥ 7, naive height 39.25
2026-05-28 05:01:18 · David Renshaw

submitted curve #43 — rank ≥ 6, naive height 35.18
2026-05-28 04:36:54 · David Renshaw

commented on curve #41

Found by Brumer - McGuinness. A rank 5 example from their elliptic-curve examples page, with independent points of x-coordinates 5, 4, 3, 7, 0.
2026-05-28 04:36:54 · David Renshaw

commented on curve #42

The standard conductor 37 rank-one curve y^2 + y = x^3 - x, with generator [0, 0].
2026-05-28 04:35:40 · David Renshaw

submitted curve #42 — rank ≥ 1, naive height 11.61
2026-05-28 04:35:25 · David Renshaw

submitted curve #41 — rank ≥ 5, naive height 25.19
2026-05-27 22:32:12 · David Renshaw

commented on curve #40

Found by Elkies - Klagsbrun (2020). A curve of rank exactly 20, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:11 · David Renshaw

commented on curve #39

Found by Elkies (2009). A curve of rank exactly 19, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:10 · David Renshaw

commented on curve #38

Found by Elkies (2006). A curve of rank exactly 18, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:09 · David Renshaw

commented on curve #37

Found by Elkies (2005). A curve of rank exactly 17, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:08 · David Renshaw

commented on curve #36

Found by Dujella (2002). A curve of rank exactly 15, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:07 · David Renshaw

commented on curve #35

Found by Fermigier (1996). A curve of rank exactly 14, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:06 · David Renshaw

commented on curve #34

Found by Schneiders - Zimmer (1991). A curve of rank exactly 11, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:05 · David Renshaw

commented on curve #33

Found by Schneiders - Zimmer (1991). A curve of rank exactly 11, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:04 · David Renshaw

commented on curve #32

Found by Kretschmer (1986). A curve of rank exactly 10, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:03 · David Renshaw

commented on curve #31

Found by Kretschmer (1986). A curve of rank exactly 10, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:02 · David Renshaw

commented on curve #30

Found by Brumer - Kramer (1977). A historical rank ≥ 9 record, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:01 · David Renshaw

commented on curve #29

Found by Grunewald - Zimmert (1977). A historical rank ≥ 8 record, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:32:00 · David Renshaw

commented on curve #28

Found by Penney - Pomerance (1975). A curve of rank exactly 7, via Dujella's elliptic-curve rank-records tables.
2026-05-27 22:31:59 · David Renshaw

commented on curve #27

Found by Penney - Pomerance (1975). A curve of rank exactly 7, via Dujella's elliptic-curve rank-records tables.