curve #3963

y² = x³ + x² − 458754970469636492277040x + 114786521606836319256741604057154900

a-invariants: [0, 1, 0, -458754970469636492277040, 114786521606836319256741604057154900]
c-invariants: [22020238582542551629297936, -99175554668438701269320001215157621184]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 536728523406795140805407760
discriminant (Δ): 487050243034594509266852843153263051024593865379213165727764505600000000
Faltings height: 12.5174
naive height: 175.0620
primes of bad reduction: 2, 3, 5, 11, 31, 59, 101, 149, 199, 389, 1301, 3001, 24439
regulator: 6045593265705.4607040584935732819992930564924799325807951
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:35:21 UTC
last updated: 2026-10-05 04:35:21 UTC

Witness: 9 independent points log in to add more points →

(11623873831860519888770/15999973081, -821948000821724102313788496000000/2023852594988771)
(1249013211822905/2704, -5330318119437843494325/140608)
(335356926212617970/323761, -159639574821887141426649600/184220009)
(2253102218368862591105/4436625664, -33414763471469157058303849365825/295514762227712)
(11340369117581986505/8479744, 33975274682565829589920769925/24693014528)
(18833195780511705009911971/36009756660969, -28922104189208289987985487024974121380/216087815897979367797)
(3301642414588534226/4068289, 4318667323126368863997991680/8205738913)
(974096670159694568857596770/1902295179165481, -9866933536136664546019801125405338400000/82969192048512815948629)
(6408657376201715638419266/1560113412025, 16015283258065986844911795899920740864/1948651856722766125)

Commentary

Unlisted rational-isogeny neighbor of curve#3673 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:35:21 UTC · history