curve #5770

y² = x³ − 10050783801671550526875

a-invariants: [0, 0, 0, 0, -10050783801671550526875]
c-invariants: [0, 8683877204644219655220000]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 1608125408267448084300
discriminant (Δ): -43639886172071473595533804498803110922018750000
Faltings height: 7.6282
naive height: 114.8470
primes of bad reduction: 2, 3, 5, 11, 13, 17, 29, 41, 89
regulator: 122443099.4276284355030259980252782706389753737202885
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:28:31 UTC
last updated: 2026-10-25 01:28:31 UTC

Witness: 7 independent points log in to add more points →

(11174746441/16, 1181272544631739/64)
(589316614915759/26801329, -3342384673520752565902/138750480233)
(5571490159/49, 414445366179298/343)
(22293379, 32076602992)
(4782301278199/90601, -10094472799460266582/27270901)
(90978925519/529, 27414589021038478/12167)
(12192444082699/3481, -42573181663941781832/205379)

Commentary

Voznyy (2026), A^2 = 38587627650^2, [r, s, t] = [18, 39, 41] or [25, 33, 54] or [13, 17, 78] or [29, 41, 89] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:37:34 UTC · history