curve #6461

y² = x³ − 15436903020771556x

a-invariants: [0, 0, 0, -15436903020771556, 0]
c-invariants: [740971344997034688, 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): 246990448332344896
discriminant (Δ): 235429294601998045159098338237834453206140892647424
Faltings height: 8.3549
naive height: 123.4402
primes of bad reduction: 2, 31, 37, 41, 1321
regulator: 193741.278569723403280875107613876634234059702687
submitted by: David Renshaw
submitted at: 2026-11-03 18:35:08 UTC
last updated: 2026-11-03 18:35:08 UTC

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

(-30640958, 666508569144)
(387810062, 7234552203816)
(-1031437456/25, 94096049910072/125)
(90386831998/9, 27172181716814008/27)
(825734771926/1089, 740203074134889920/35937)

Commentary

Congruent-number curve y^2 = x^3 - n^2 x, n = 124245334. 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 18:39:51 UTC · history