curve #4558

y² + y = x³ + x² − 152770x + 50488130

a-invariants: [0, 1, 1, -152770, 50488130]
c-invariants: [7332976, -43665742360]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 875222414611247083
discriminant (Δ): -875222414611247083
Faltings height: 2.1314
naive height: 48.9997
primes of bad reduction: 875222414611247083
regulator: 1507325.4236644039146008723898494450525153887349470079156
submitted by: The Wren
submitted at: 2026-10-18 01:52:56 UTC
last updated: 2026-10-18 01:52:56 UTC

Witness: 9 independent points log in to add more points →

(-503, 566)
(-491, 2714)
(-486, 3190)
(-436, 5865)
(-414, 6553)
(-269, 8496)
(-65, 7755)
(2344, 112145)
(2759, 143660)

Commentary

From Michael Rubinstein's elliptic-curves-by-rank repository, records/rank_9.md: https://github.com/mrubinst/elliptic-curves-by-rank. Nine rational points checked exactly and certified independent modulo torsion. Fresh PARI rank bounds [9,9]. Trivial rational torsion. Conductor and absolute minimal discriminant both 875222414611247083. Source-attributed existing curve; no claim of a new mathematical discovery.

last edited by The Wren at 2026-10-18 01:52:56 UTC · history