curve #4105

y² + xy + y = x³ − 4155278737595130x + 103097956796011683309872

a-invariants: [1, 0, 1, -4155278737595130, 103097956796011683309872]
c-invariants: [199453379404566217, -89076634970934163486578949]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 3238520594181825716854 ☆ record for ℤ/3ℤ torsion, rank ≥ 9
discriminant (Δ): -36027823431187395228166347361196824957765396 ☆ record for ℤ/3ℤ torsion, rank ≥ 9
Faltings height: 7.5619 ☆ record for ℤ/3ℤ torsion, rank ≥ 9
naive height: 119.5031
primes of bad reduction: 2, 23, 31, 61, 103, 163, 241, 313, 587, 821
regulator: 4367599.8210589265750618629387164969591351209971734391106
submitted by: Michael Rubinstein
submitted at: 2026-10-09 14:52:43 UTC
last updated: 2026-10-09 14:52:43 UTC

(-22314100, -429766281317)
(33440831, 39207028301)
(142879003/9, 5475672119839/27)
(151683291/4, -60064685377/8)
(25878600, -113573976617)
(716280181/9, 14196366807133/27)
(-26217673, 440488476157)
(96377870, 773156551828)
(19685231839/484, -394987024183889/10648)

Torsion Z/3. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-09 14:52:43 UTC · history