curve #5774

y² = x³ − 7409361153114084675

a-invariants: [0, 0, 0, 0, -7409361153114084675]
c-invariants: [0, 6401688036290569159200]
rank (lower bound): ≥ 7
torsion subgroup: trivial
families: y² = x³ + k (Mordell curves); x³ + y³ = A (cube-sum curves)
conductor (N): 2400633013608963434700
discriminant (Δ): -23716209325223265923753975172846177630000 ☆ record for cube-sum curves, rank ≥ 7
Faltings height: 6.4261 ☆ record for cube-sum curves, rank ≥ 7
naive height: 100.4217 ☆ record for cube-sum curves, rank ≥ 7
primes of bad reduction: 2, 3, 5, 7, 23, 43, 83, 547
regulator: 4110122.153400095290744527403968550434098454815968412
submitted by: Maksym Voznyy
submitted at: 2026-10-25 01:47:09 UTC
last updated: 2026-10-25 01:47:09 UTC

(1073004499/9, 35148060474632/27)
(63437223889/29584, 7965162533695513/5088448)
(1554636148954651/199402641, 60816484127141912099924/2815764693561)
(14911872571/625, 1820454301786756/15625)
(2427792320223991/971506561, -86694593110198256981686/30280887999809)
(63432439, 505197056938)
(51330224551/14641, 10582566478337426/1771561)

Voznyy (2026), A = -28288001070, [r, s, t] = [-18, 1, 23] for S2 in https://arxiv.org/pdf/math/0403116

last edited by Maksym Voznyy at 2026-10-25 01:47:10 UTC · history