curve #6091

y² = x³ + x² − 755532816798465189546809104536733853585x + 7989847940316878801621318162157864877065367322947023727983

a-invariants: [0, 1, 0, -755532816798465189546809104536733853585, 7989847940316878801621318162157864877065367322947023727983]
c-invariants: [36265575206326329098246837017763224972096, -6903228620433783284818412343342353228373958389132807850809856]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 38108330957491470085780912737156432881247314621760
discriminant (Δ): 24089703607477327530085267350902516670105832293822661623835593101403375582262831044117657277258523292630806784000000
Faltings height: 21.0919
naive height: 280.1751
primes of bad reduction: 2, 3, 5, 7, 11, 41, 43, 59, 109, 151, 227, 233, 347, 353, 433, 521, 557, 641, 881, 1559, 19853, 21163
regulator: 2483526009262879.659396791636062717616695922318197712425270044923
submitted by: The Wren
submitted at: 2026-10-29 02:06:24 UTC
last updated: 2026-10-29 02:06:24 UTC

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

(14626753728175201711, 8254171010364237089079009600)
(-415882311129619850738093281529/14588049961, 140507163420169743941501249323794467525496000/1761959262339541)
(-3733046429655378075799646759/195748081, 340554610078172559047247374965799554322400/2738711401271)
(-1459222151614544636430923/63001, 1807398901162947657367443922382375820/15813251)
(-1224457679394774288569/121, 160820800292875452408138754467600/1331)
(-23781208640913292067/4, 886217039064514323433840895685/8)
(376713965734675424149/25, 644038817486951915528883820668/125)
(4903919969530161762917551/319225, 530442036865350620989149211231349376/180362125)
(7865780035255888092790471/516961, 1514647271101089323684193310845396000/371694959)
(4162620805916161678497025639/253032649, 14398135262044230410638327434764949585600/4024990347643)
(462952838247993543820678987021/24690961, 314995725237741793909701836074323547940955900/122689385209)
(220643690783808519056854517995831/14307011216521, 132079377906924966017803720552854888219936639600/54115711953053238181)
(139026952610292183613005797473855321/6479904820596736, 21227054333804738838321830758673503310483713179677475/521618445142101888598016)

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=4796/196149 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 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 02:06:24 UTC · history