curve #1639

y² + xy = x³ + 418429693733415381360x − 8896829519920563914931292262400

a-invariants: [1, 0, 0, 418429693733415381360, -8896829519920563914931292262400]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/8ℤ
conductor (N): 503432816707590
discriminant (Δ): -38882990829482360019296008558230635514530722089683179263900000000
Faltings height: 11.0759
naive height: 156.0496
primes of bad reduction: 2, 3, 5, 7, 11, 31, 41, 181, 809, 1171
regulator: 19240.05977850422291365365073213621429980659887
submitted by: Michael Rubinstein
submitted at: 2026-09-25 02:09:19 UTC
last updated: 2026-09-25 02:09:19 UTC

(1219162970880, 1346333040895714560)
(8816227363050/529, 20013000614814336180/12167)
(13100620448012280/39601, 1502148659724794665320840/7880599)
(3206628715676144635689705/44629133694016, 5903687567195335801148190481499502465/298145106159408664064)

Torsion Z/8. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 02:09:19 UTC · history