Elliptic Curve Rank Leaderboard

← home · all curves · JSON ↓

curve #4096

y² = x³ − x² − 2285162669176x + 318639106356309376

a-invariants: [0, -1, 0, -2285162669176, 318639106356309376]
c-invariants: [109687808120464, -275303529765002578112]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 825030649904725540797360
discriminant (Δ): 719853896926134270305087550901440537600
Faltings height: 6.1468
naive height: 96.9860
primes of bad reduction: 2, 3, 5, 7, 17, 23, 59, 61, 269, 8689, 21329569
regulator: 2184041.006599097595305587856530816245100724798251947458721
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:50:51 UTC
last updated: 2026-10-09 14:50:51 UTC

Witness: 10 independent points log in to add more points →

(-303732, -992318404)
(-1514884, 551294820)
(1652236, 1026362820)
(23375800, -112783388976)
(-625704, 1226176000)
(-828242, -1281852054)
(409342/9, 12513514258/27)
(-237239, -920552220)
(6616024, 16576942080)
(1470838, 373485546)

Commentary

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-09 14:50:51 UTC · history

Log in to edit commentary.