curve #6458

y² = x³ − 3022289217573201x

a-invariants: [0, 0, 0, -3022289217573201, 0]
c-invariants: [145069882443513648, 0]
rank (lower bound): ≥ 5
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 96713254962342432
discriminant (Δ): 1766802638780509052861871058716392562105308134464
Faltings height: 7.9472
naive height: 118.5480
primes of bad reduction: 2, 3, 73, 373, 673
regulator: 279612.917988424411005004254566722117333134808203
submitted by: David Renshaw
submitted at: 2026-11-03 18:34:55 UTC
last updated: 2026-11-03 18:34:55 UTC

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

(-5963151, 133455319380)
(-52650865728/961, 1001075041733256/29791)
(497664433/4, 9959473917953/8)
(3116668937281/56644, 226641317117140295/13481272)
(36211618076881/108900, 214908635426221171279/35937000)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x, n = 54975351. Found in a local squarefree-parameter search using Monsky 2-Selmer matrices and Mestre-Nagao scoring, followed by PARI/GP ellrank point search. Search performed 2026-11-03. Method reference: Dujella, Janfada, Salami (2009), https://web.math.pmf.unizg.hr/~duje/pdf/Sajad_JIS.pdf.

last edited by David Renshaw at 2026-11-03 18:39:44 UTC · history