curve #2179

y² + xy = x³ − 590353702194591280765010561772238260x + 174588372339329184400865798305984325852297773091859600

a-invariants: [1, 0, 0, -590353702194591280765010561772238260, 174588372339329184400865798305984325852297773091859600]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/2ℤ × ℤ/8ℤ
conductor (N): 1565117437821917694330
discriminant (Δ): 74837036235453814811572246475871672573324843483088588564423513916440631640375942776949250654233600000000
Faltings height: 19.1543
naive height: 258.7117
primes of bad reduction: 2, 3, 5, 7, 11, 19, 67, 239, 1151, 39679, 48761
regulator: 208305.99874409815681806634855818933604505043
submitted by: Tom Fisher
submitted at: 2026-09-26 16:54:54 UTC
last updated: 2026-09-26 16:54:54 UTC

(4043145978848660830/9, 174836140793270820642525880/27)
(-344320394143837595000245442992956696/814862753036115169, -434298487065859430358209850792879439798635022311026124/735574559415602783298880303)
(1451737788330638657633482779601154870036516263378345751837531961063344239611753112849556760/3155136161424248768625112088369105899244411500618381837275221737203503929, 107360513440730689070029083206307720462995748894071425185832190680260396195579613118258628735894896986022984370130847040150217732224660/5604374640684366142548869049661504017759384690908932215403119227589334003883898544252546288500646931113819283)

Found by Campbell - Goins (2003). The third independent point was found by M. Watkins (March 2005).

last edited by Tom Fisher at 2026-09-26 16:54:54 UTC · history