curve #3950

y² + xy = x³ − 228888687304891183515x + 1323763366064832362681250762600

a-invariants: [1, 0, 0, -228888687304891183515, 1323763366064832362681250762600]
c-invariants: [10986656990634776808721, -1143731548296495146842552824099481]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 17261904761372158878705
discriminant (Δ): 10440107546791480674862006427899703091788213355267860485280625
Faltings height: 10.5366
naive height: 152.2529
primes of bad reduction: 3, 5, 11, 13, 19, 43, 71, 151, 163, 337, 739, 1741
regulator: 1372500091.03567767373765983152549505327948672227970178
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:32:48 UTC
last updated: 2026-10-05 04:32:48 UTC

Witness: 8 independent points log in to add more points →

(-4700950600, -1515211089600160)
(129700249973085/21904, 1360213434543544418145/3241792)
(35378233447125/4624, -44920569372713538195/314432)
(122216640093996345/22505536, 52405367514696862109217105/106766262784)
(22849998162345/3136, -36348922548517158105/175616)
(549159928500/49, -139844513391042930/343)
(281206670766477/13456, 3715903644014179346931/1560896)
(1345009833252905/341056, -138343963478812099373735/199176704)

Commentary

Unlisted rational-isogeny neighbor of curve#3670 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:32:48 UTC · history