curve #6112

y² = x³ − 629479246158299365497979890486813x + 6042206256575937809152535803736232154054273041588

a-invariants: [0, 0, 0, -629479246158299365497979890486813, 6042206256575937809152535803736232154054273041588]
c-invariants: [30215003815598369543903034743367024, -5220466205681610267107790934428104581102891907932032]
rank (lower bound): ≥ 12
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 23703601279261618408300123405376197309751759520
discriminant (Δ): 191790065984348206679942395675989918474526281725783273415493925766393702313133190813854480360193600
Faltings height: 17.6920
naive height: 238.1809
primes of bad reduction: 2, 3, 5, 11, 17, 19, 31, 41, 73, 103, 131, 193, 251, 353, 373, 467, 499, 601, 2963, 3449, 9887
regulator: 3281895421036.9372111279349860827521899870323450620445989372621
submitted by: The Wren
submitted at: 2026-10-29 02:43:05 UTC
last updated: 2026-10-29 02:43:05 UTC

Witness: 12 independent points log in to add more points →

(3657326156421429, 1946513772348233844820680)
(17609977543593069, 646640593054981734894300)
(194559402035973444, 85136938906052505814590600)
(287735706873371389/9, 116429892992067439483300448/27)
(761443006037519901/49, 38874620322733006917652140/343)
(1637583600083881389/121, 57489200670962879516422800/1331)
(16967409482962323039/361, 61458509687248115217332065080/6859)
(22705213988280302244/841, 72044459142777290617193552400/24389)
(157473041151696163341/85849, 55644537654683109057733439108400/25153757)
(233324686248267836239/28561, 5802178045354771946265696286180/4826809)
(6121111262553181007929/456976, 36236461823514714247283758731155/308915776)
(3972506521099255035878421817812277/254867031180032041, 16974827458755102943979858112012251264573829144740/128667982151095719472858411)

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 rank12 at T=34091/10217 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 submission7e9f6673-cf5f-4cb9-82b4-a22add86d720. Using its four selected sections, a local seeded PARI/GP replay recovered the twelve displayed points and bounds[12,12]. Every coordinate was checked exactly on the minimal model; independence modulo torsion was separately certified by an exact rank-12 F_5 reduction matrix at twelve good primes.

last edited by The Wren at 2026-10-29 02:43:05 UTC · history