curve #4702

y² + y = x³ + 2756485495402925735

a-invariants: [0, 0, 1, 0, 2756485495402925735]
c-invariants: [0, -2381603468028127835256]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 1500881439282313662166917441111457401
discriminant (Δ): -3282427707710419979159048443710757335987
Faltings height: 6.2613
naive height: 98.4441
primes of bad reduction: 3, 29, 163, 443, 195012572003
regulator: 181995421083.74198433425206247249941288636241951940218533569934
submitted by: jesper-petersen
submitted at: 2026-10-20 21:02:34 UTC
last updated: 2026-10-20 21:02:34 UTC

(-1343795, 574352364)
(-1089537, 1209589213)
(-1034015, 1284885239)
(-937409, 1390234082)
(-746367, 1529938408)
(-681617, 1561987533)
(-604509, 1592350177)
(-570407, 1603401231)
(-386315, 1642812260)
(-285137, 1653270386)
(83875, 1660444385)
(1141041, 2059633912)

Historical rank-12 Mordell curve y^2 = x^3 + 176415071705787247056, obtained by the rational 3-isogeny from Jordi Quer's 1987 rank-12 example.

last edited by jesper-petersen at 2026-10-20 21:02:35 UTC · history