Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #1909

y2 = x3 − 2289196x + 13734960
a-invariants
[0, 0, 0, -2289196, 13734960]
rank (lower bound)
≥ 5
torsion subgroup
ℤ/2ℤ × ℤ/2ℤ
conductor (N)
3463390144
discriminant (Δ)
767684562531605807104
Faltings height
2.6970 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 5
naive height
55.5447 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 5
primes of bad reduction
2, 17, 47, 89, 761
regulator
619.076295241879719210365824198152207582906685956
submitted by
Natanael Wildner Fraga
submitted at
last updated

Witness: 5 independent points log in to add more points →

Commentary

Found on 2026-09-25 in a AI-assisted computational search in the family y^2 = u(u+a)(u+b), with a = 1504, b = 3026 and x = u+1510. The five submitted points were verified to be independent modulo torsion by exact full 2-descent: the square-class matrix has rank 7, including two torsion rows of rank 2. An additional certificate using quadratic characters at good primes gives the same ranks. The torsion subgroup is exactly Z/2Z x Z/2Z, verified using good-prime reduction counts. This proves rank >= 5. Comparison data were obtained from the ICARM Elliptic Curve Rank Leaderboard, supported by NSF Grant DMS 2425401.

last edited by Natanael Wildner Fraga at · history

Log in to edit commentary.