curve #150

y² + xy = x³ − x² − 1743349x + 886895689

a-invariants: [1, -1, 0, -1743349, 886895689]
rank (lower bound): ≥ 9
torsion subgroup: trivial
conductor (N): 183107934630169474
naive height: 54.7286
Faltings height: 2.3121
discriminant (Δ): -366215869260338948
primes of bad reduction: 2, 244254379, 374830403
regulator: 293591.30673220840727887138511462027952831615032133636905
submitted by: Edgar Costa
submitted at: 2026-06-24 21:06:39 UTC
last updated: 2026-07-01 22:53:26 UTC

Witness: 9 independent points

(-28, -30575)
(56, 28069)
(-87, -32173)
(130, 25673)
(-159, -33980)
(176, 24109)
(264, 20963)
(-285, -36743)
(-302, -37075)

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 21:11:37 UTC · history