curve #1084

y² = x³ − 81634669486808209634997359691482434636287x + 8977596286871042598609967051908212510016658847188545565102434

a-invariants: [0, 0, 0, -81634669486808209634997359691482434636287, 8977596286871042598609967051908212510016658847188545565102434]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1544209591355171508263116235415332449383972946440
discriminant (Δ): 77409501948973198317001430574073989940536486795252492314829388942204317042488280067788467662745710255329075360000
Faltings height: 21.8323
naive height: 294.2228
primes of bad reduction: 2, 3, 5, 7, 11, 13, 23, 43, 47, 53, 73, 89, 317, 1319, 1367, 1987, 1993, 2281, 6221, 27481, 303313
regulator: 177779721425.2079650924217424226082612559965607737352473745
submitted by: C. R. Hill
submitted at: 2026-09-23 17:15:18 UTC
last updated: 2026-09-23 17:15:18 UTC

(162602604340593389143, 52300762410704501849143965760)
(164984045926475906973, 551453736181936832009844750)
(177206175739093403913, 275793617262026874422316858030)
(59549881090154691261345/361, 172239516266057855707454174358/6859)
(570799616133545344084563/1681, 311361373951990006927406672901553200/68921)
(235910342109329286050597637/1408969, 92329942750540720684149475377216473850/1672446203)
(98893595621003375953999596013/599809081, 27491994190905203182010605436285044691950/14689924202771)
(17464066381308599452453449508143/105923560681, 65195101402811059705833869660020343138904960/34473776135677579)
(1077650388206334070181148679539213/6532834395481, 35707587231014782691169328456223563026174450/16697539277620102621)
(786880074494543742402474810528170517/4770143712015529, 334925833269966785717105157297989208425995559850/329455828436687153439083)

Found with Rank Hunter v0.8.10; family=DMT Triad Family - CEF; parameter=-463/191; local status: rigorous rank lower bound >= 10.

last edited by C. R. Hill at 2026-09-23 17:15:18 UTC · history