curve #3835

y² + xy = x³ − 86279071033271990371380695302843708152938312838660x + 309717542950116143203092073265175193957219136338722107274038852847797075472

a-invariants: [1, 0, 0, -86279071033271990371380695302843708152938312838660, 309717542950116143203092073265175193957219136338722107274038852847797075472]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 17706651565185254682234696532020031728638902470674988528322932884674811227970677970816681829581589913401166117781970 ★ record for rank ≥ 29
discriminant (Δ): -334420015912268214200810106377904048771967504713126998535223490080565166404699561661838866992348673483829058749679384888791517473502503724083200000000
Faltings height: 27.5410
naive height: 356.5667
primes of bad reduction: 2, 3, 5, 7, 13, 19, 23, 71, 109, 179, 114327172294589, 981816477871970142827645414962319781895481, 13635675611390540081659886416309134170462804299
regulator: 59607911221254654915722299670301.5513022982787944937527297533977535855786049775438594790026818497
submitted by: Matej Jurasić
submitted at: 2026-10-03 09:04:45 UTC
last updated: 2026-10-03 09:04:45 UTC

Witness: 29 independent points log in to add more points →

(4115708251087284864326934, -4932977234414800900369019930752743342)
(9632481061248161387351784, 19297222802229311250592831292747595708)
(4960209511410092693704584, -1947992242322831051798367475266989892)
(-6116239971561318415961616, -24670272540513189242478061902082872492)
(-7530129816467908537996216, -23074450995903342389044049197473708292)
(-4592264901261037055362296, -24679710116248832611867096833772856772)
(4992581011040213670221384, -1845722703941239483103205447685063492)
(11357779759147602690069234, -28194377395756390749330683848219719192)
(-10128707222308540418325816, -12020887138151122034892497933320969092)
(7211161771467180828281964, 7907703545623530945542108250066445548)
(5588818560076596290402184, -1444167081925425565199491077354625092)
(18835696602790239429424584, 73261073379445595679014414789168005308)
(7975153922472970224513012, -11352225544366562580947012572540563360)
(90194881260537872835197949/16, -100869752776037916990939632935140759543/64)
(14009491805989559298046911/4, 56849737878398505019352229496847074689/8)
(1533247363171549656702840456/2209, -1642131963367216247216424903887997462910716/103823)
(968030621392892726369684, 15069966340978500086573561912994377408)
(15141629223114010270733034, -49747533143137644196089562802875416792)
(-9512832210519386270513736, 16420166043245734064397638267902245948)
(664880889316813930753493264/121, -1649155765501323675817954799869801980452/1331)
(-9979342864881054862503816, 13300763988891645257165098213672846908)
(26907435319120272697836584, 132171945946779260548880393784991346108)
(-5351874915127641234496116, 24863244221375188932450962820375312108)
(1528314154056672670938232056/169, 36036110294645005363590830721181663275756/2197)
(25101948523230992314066636116/2809, 2364875556296884746904756557930772680101856/148877)
(48559772313212764977614952, 332605575442007357696047341008756591580)
(-9893557439674681180924728, -13961323776553470562978100793667853700)
(1399600287156182711996574072, -52359621016151521907774676453002054526900)
(23040000462013229793762707016/49, -3496548978957674252174797243327898848406556/343)

Commentary

Specialization at T = 4157/637 of a rank-16 fibration of X1092 (three neighbour steps from the one in curve#1879).

last edited by Matej Jurasić at 2026-10-03 09:04:45 UTC · history