curve #6097

y² = x³ + x² − 145237969955437674311840688277721469119433x + 12789701555357129044480579973453268392854898766363723877414263

a-invariants: [0, 1, 0, -145237969955437674311840688277721469119433, 12789701555357129044480579973453268392854898766363723877414263]
c-invariants: [6971422557861008366968353037330630517732800, -11050302143828559494473049632410789941628442652362241213192320000]
rank (lower bound): ≥ 13
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 60683857455542064605589057157930052320159888388875200
discriminant (Δ): 125409181291379724073823552163902947202768908046737111671588808487447865375573062674336797964794785955000400345453675584000000
Faltings height: 22.7042
naive height: 295.9512
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 37, 43, 67, 71, 101, 103, 127, 139, 149, 191, 199, 227, 379, 643, 1231, 2179, 4327, 4373
regulator: 21962198993247.45155513198861912112581408627860334812425233884906
submitted by: The Wren
submitted at: 2026-10-29 02:26:33 UTC
last updated: 2026-10-29 02:26:33 UTC

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

(-254071943519929949217, 5769714237814869019999132026600)
(52886569926345268443, 2292702918045204158324157373200)
(383793968991632781282, 3685139886762435736715271082857)
(660934924541230601823, 14335841298512574030143172403800)
(1108794490879985465193, 34855853953387950739107118875300)
(293813169214827575965443, 159259930312251482516488174535554200)
(-157860573722339828099053522107/644093641, 94842895354054507422130713120832926649487400/16346452514939)
(-70433589815477041447857387/177241, 207740436918461251616317556647295483400/74618461)
(56313457557213872085631/729, 28053458877456145659720932202912832/19683)
(4715599913622357740819296557/4592449, 302744793157575252518064960864276037819200/9841618207)
(46056732521301541324776867167/140968129, 772680872093554370056882447476795131537400/1673714595617)
(98977043355759078089188071507/13126129, 31099458258345961749003243226710638088562200/47555965367)
(2017727488384615982269844581659/60226558921, 41704175198040061983630411941263134017352486936/14780260051361531)

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=-14707/17361 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_7 reduction matrix at thirteen good primes.

last edited by The Wren at 2026-10-29 02:26:33 UTC · history