curve #6110

y² + xy + y = x³ − 1888917861063328433650553035253654128993868x + 543972026037092864862959201260987745247989378817477999755285306

a-invariants: [1, 0, 1, -1888917861063328433650553035253654128993868, 543972026037092864862959201260987745247989378817477999755285306]
c-invariants: [90668057331039764815226545692175398191705641, -469991830496048235241732751975489971541485663116839254885854063061]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 11643434205218962024218516421340879789523637819129098777570
discriminant (Δ): 303508259101253649720879892876525517385597748152059781777716368919527946782382308003112084401392329176208262783052057287656250000
Faltings height: 23.3511
naive height: 303.6473
primes of bad reduction: 2, 3, 5, 7, 11, 19, 29, 31, 37, 61, 67, 71, 79, 109, 137, 181, 193, 197, 199, 229, 271, 307, 677, 691, 1009, 2609, 6389, 113489
regulator: 65883103304984.71342619944290100036285668336141201929900426066420
submitted by: The Wren
submitted at: 2026-10-29 02:32:57 UTC
last updated: 2026-10-29 02:32:57 UTC

Witness: 13 independent points log in to add more points →

(-1375421292231678134940, 23238550887834679965494877546382)
(-1242902089945667884740, 31171619593391155565012022785182)
(-497141567599086933915, 36880390511389301564203995212107)
(15367701007650932475885, 1897589977655633447261713616268307)
(28061037498070114314357, 4695041250960773984403552581731279)
(-124575592951377234442931757315/406264336, 270889107048358347945466667368543270022348087/8188663956416)
(-103022698039446143737275/169, 84203387691488762495928281367822079/2197)
(331578540700477633840/9, 588098433344859918553018959885539/27)
(176203850820853017558102/121, 39514423084761983275167521522274173/1331)
(1122875097459411203570580/49, 1187748625113672079868765692711166626/343)
(2021528377733646059781160/81, 2869907183238769949660624557489896553/729)
(976563410149059737343990171465/44182609, 963208779392991718109802995055923669665735061/293681802023)
(62264927250370395814449398491965/1298016784, 491120396064210623310723684044554487142953927389/46764948693952)

Commentary

Source parameter/search by bufferhe4d (2026), public Yukon submission 15009775-297e-4a19-9179-4a455b778310: https://raw.githubusercontent.com/Layr-Labs/elliptic-rank-challenge-public/6837b3bcd53a73fb5af3e271d91dec3148236631/submission/search/x400a-opus/xlog.txt . The source log records rank13 at T=113489/74391 in the rank-five X400a family posted by wgxli with curve#4252: y^2=x(x+A)(x+B), A=q(121q-99p)(26p-23q)(75p-44q), B=p(21q-74p)(25p-36q)(p+77q). The published section code credits 0xArion submission 7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the thirteen displayed points and bounds [13,13]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-13 F_5 reduction matrix at thirteen good primes.

last edited by The Wren at 2026-10-29 02:32:57 UTC · history