curve #4182

y² + xy = x³ − x² − 331974883793761714x + 87521530701989517132845344

a-invariants: [1, -1, 0, -331974883793761714, 87521530701989517132845344]
c-invariants: [15934794422100562281, -75618602454812367903325846965]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 1674082798132520510297902122116529654619101614365726
discriminant (Δ): -967619857320596854952187426583354140369840733103389628
Faltings height: 9.0777
naive height: 132.9910
primes of bad reduction: 2, 17, 308537, 2617621165669818557, 60965476248586842423523171
regulator: 1762179431238121.90563777509555032241538198246036899395457742944670614098
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 23:02:01 UTC
last updated: 2026-10-11 23:02:01 UTC

(53322648978, -12312416134576418)
(-112286726, -11107696004952)
(27980826985/9, 4606294496747566/27)
(6347886776, -503761559644220)
(-528050930, -10750578969418)
(15870402192, 1998014047063040)
(591411427, 9901435091385)
(2467863421/16, 404699352857681/64)
(574324024, -9290069643372)
(25860130214/49, -2641739614312548/343)
(235059538696846/674041, -2082625610641643039106/553387661)
(239734626, -4659932107106)
(5915133013/16, -250512597870027/64)
(222277520, 4971116878032)
(-290736637653/529, 124061750577761119/12167)
(1220842926378/961, 1234078738716252962/29791)
(46707314030144952/76615009, -7088189350579243660917820/670611173777)

No commentary yet.