curve #3821

y² + xy = x³ − 142556915057809820669404431347084412460865025x + 638563090201241987261011521253095774638694270961241699322950715657

a-invariants: [1, 0, 0, -142556915057809820669404431347084412460865025, 638563090201241987261011521253095774638694270961241699322950715657]
rank (lower bound): ≥ 27
torsion subgroup: trivial
conductor (N): 1277414651849224714944188643218143283375500620355530661526191773059704994595744251834510121308007020963792790
discriminant (Δ): 9261450754788381950932538719840196155675782237564127455197105460360059339294558767918263041666583428781544179229668138613765017600000
Faltings height: 24.2919
naive height: 316.6185
primes of bad reduction: 2, 3, 5, 7, 11, 13, 43, 71, 191, 6631682173483378220261500900898852856969937626059790061182280482167497478322792050628542795337581
regulator: 364202867121394018536287853640.39785974096088621298217952306357699466012913685213730702613242
submitted by: 7fff-zip
submitted at: 2026-10-03 05:01:41 UTC
last updated: 2026-10-03 05:01:41 UTC

Witness: 27 independent points log in to add more points →

(8580404275062501033834, -216991075467293214568993600929237)
(-13746018824452575516846, 28304989110211226087556356803323)
(5465912194116513222954, -150532968097157954277332722769877)
(52137804089119312469454, -11616143525484398212299478699310877)
(-10833529831566441726486, -954712763149701455720798219064597)
(74405076937167044551194/25, -61319772395975109305829973802848257/125)
(3826319835730456284398, -386153892998302959025725709947409)
(-1184137700058196487286, -897613352755970408844480002954997)
(2823307356540906770827281/64, 4585149300414396317122251750138283101/512)
(24065637245898648744354, -3338498423417313561109306644914877)
(5842683188078663714154, 71411235955803544544463650209323)
(661278575771746759914, 737958282375526427918506247898603)
(35292315226739584138674, 6290123607864976919261349432122043)
(-12183559445251210503666, 752925552373995040459387194357903)
(59113312823190165825834, 14098799646984460912351406148767403)
(-8012803235327622766486, -1125336146649562579058919353584597)
(5933705332330708538154, -39891821009114649498887031771477)
(5024851793390421197754, -221605243488219468972482081596677)
(5198567574445135255914, -194841391173938964405393673853397)
(-3177090779479833440676, -1029276491262777830790589863734517)
(16311389912402000751114, -1628831963944927947705212864635797)
(8223401217417178708464, -149540493294501451655226294803997)
(8211301021091041278954, 147092260781238947840861784486123)
(-1187302138998893712246, -897857169451713908332350679126677)
(3102740239576423972074, -475516649953950042610965572522517)
(11595008943751415884404, -737900035438731708562959498076677)
(7858114519252561005354, -59773014379514587842532686401877)

Commentary

X1008 at T=924/1615

last edited by 7fff-zip at 2026-10-03 05:01:41 UTC · history