curve #5033

y² = x³ − 2141283076x

a-invariants: [0, 0, 0, -2141283076, 0]
c-invariants: [102781587648, 0]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
families: y² = x³ + ax (quartic twists); y² = x³ − n²x (congruent-number curves)
conductor (N): 34260529216
discriminant (Δ): 628350879731489748444432830464
Faltings height: 4.4072
naive height: 76.0676
primes of bad reduction: 2, 17, 1361
regulator: 3711.875844001787077507943193627090324583513300
submitted by: David Renshaw
submitted at: 2026-10-21 01:48:51 UTC
last updated: 2026-10-21 01:48:51 UTC

Congruent-number curve y^2 = x^3 - n^2 x with n = 46274. Found in an ellrank scan of squarefree n <= 6*10^5 with n = 1,2,3 mod 8.

last edited by David Renshaw at 2026-10-21 01:48:51 UTC · history