curve #1488

y² + xy = x³ − 15875150677713173875x + 24822054816914290733556790625

a-invariants: [1, 0, 0, -15875150677713173875, 24822054816914290733556790625]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/10ℤ
conductor (N): 3471433683630
discriminant (Δ): -10114897220907125348713885612834921851511930012198502400000
Faltings height: 9.9178 ☆ record for ℤ/10ℤ torsion, rank ≥ 3
naive height: 144.2862
primes of bad reduction: 2, 3, 5, 11, 17, 31, 37, 199, 2711
regulator: 590.04331447084110738087146771286521474658186
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:32:19 UTC
last updated: 2026-09-25 00:32:19 UTC

Witness: 3 independent points log in to add more points →

(2163318590, 24560336856185)
(-5129423770930/2209, 23020900726315582135/103823)
(3017892268592078/1555009, 70507303405917071024071/1939096223)

Commentary

Torsion Z/10. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank Also found by Rathbun (2003) (see https://web.math.pmf.unizg.hr/~duje/tors/z10old3.html)

last edited by dujella at 2026-09-25 06:49:12 UTC · history