curve #4583

y² + xy = x³ − x² − 854872134455423416142706x + 222713055118201087545522356713997636

a-invariants: [1, -1, 0, -854872134455423416142706, 222713055118201087545522356713997636]
c-invariants: [41033862453860323974849897, -192424079621941087258288944743007132981]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/3ℤ
conductor (N): 1372047185460717527629907305167678 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
discriminant (Δ): 18556066559714424280044604583087760613275847900321647438214691677112055504 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
Faltings height: 12.7671 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
naive height: 176.9293 ☆ record for ℤ/3ℤ torsion, rank ≥ 11
primes of bad reduction: 2, 3, 7, 19, 29, 37, 43, 47, 103, 109, 149, 1129, 3319, 4684736527
regulator: 267362603.628960915115611908344464139548776781123337913937628
submitted by: jesper-petersen
submitted at: 2026-10-18 08:12:48 UTC
last updated: 2026-10-18 08:12:48 UTC

Witness: 11 independent points log in to add more points →

(-3754462125197/4, 3561485377228648793/8)
(-2276953286994071/2601, 72680948895296538462715/132651)
(-369072724580, 698534307782544394)
(1150136750476, -872302597509939470)
(20055809450131, -89723117174792962595)
(-1016145573184, 205340770101103854)
(-727247197796, 678073921192172890)
(-456880048765, 719665581196207744)
(-182957940739, 610732797357714234)
(773911036864, 156980600724047086)
(-5931409777964804/6889, 323696539056315486041582/571787)

Commentary

Curve and independent-point witnesses from the Layr Labs Elliptic Rank Challenge public repository, submission/board/3-11.ec. The Weierstrass coefficients and eleven rational-point witnesses are reproduced from the original public submission. The source identifies this as an independent construction without specifying further methodological details. Submitted to ICARM to document these improvements and make the curve available to other researchers.

last edited by jesper-petersen at 2026-10-18 08:12:48 UTC · history