curve #151

y² = x³ − 5347108x + 4740882532

a-invariants: [0, 0, 0, -5347108, 4740882532]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 467760769046419720
naive height: 58.0898
Faltings height: 2.6658
discriminant (Δ): 74841723047427155200
primes of bad reduction: 2, 5, 131, 62119, 1437037337
regulator: 53110.452790351633137598676208541784979819556057572982627
submitted by: Edgar Costa
submitted at: 2026-06-24 21:09:02 UTC
last updated: 2026-07-01 22:54:24 UTC

Witness: 9 independent points

(16, -68230)
(72, -66002)
(-154, -74570)
(266, -57770)
(-296, -79358)
(321, -55295)
(488, -47410)
(-519, -85885)
(534, -45142)

Commentary

Found by the ec-smallcond GPU integral-point search (Elkies-Watkins style large-rank/small-conductor sweep); rank >= 9 certified from 9 independent points via PARI/GP ellrank (returned rank exactly 9).

last edited by Edgar Costa at 2026-06-24 21:09:02 UTC · history