curve #3588

y² + xy + y = x³ − x² − 62259084497997790185923979702181161708475043947113x + 200613225836443134970778624971063932020852004282772370596096267561533256617

a-invariants: [1, -1, 1, -62259084497997790185923979702181161708475043947113, 200613225836443134970778624971063932020852004282772370596096267561533256617]
rank (lower bound): ≥ 29
torsion subgroup: trivial
conductor (N): 12971649035425791202235701899923997898689860142539308670364350398353271538805031579625311848680045272798384003916753452885038430
discriminant (Δ): -1941118914429401842751954994256258511902686332568176394857672327061253612189858537525216276437305829928432231705313189684964138644066389808926176051200
Faltings height: 27.5870
naive height: 355.6982
primes of bad reduction: 2, 5, 7, 11, 13, 17, 19, 23, 41, 67, 173, 882391, 12634339, 1642312069, 6425238277, 19336255598534327087741, 161359706569332929676074980937247310915399178625205078189321
regulator: 5572955649083424879309232540701028.81295585565420426216397720969145290198424909961732819301523694
submitted by: FNacc
submitted at: 2026-09-28 22:16:37 UTC
last updated: 2026-09-28 22:16:37 UTC

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

(8452077161612074695006587546777017/60730849, -775822334644523354894026683976787977312029997986304/473275506257)
(21604886434461178374791117, 94551836405699690401738594120689461842)
(-47705581248383273215555850927/7569, -12189272697125281338224008115546448867480224/658503)
(870496808342395367532400007, -25682245838340577525430228017531729822948)
(-76962968533872967805394570105/29929, -95991703625976590123354122172175562597621724/5177717)
(1055462365818151710896411303/289, 23016504527683295913578492754995673665116/4913)
(1205613035218259906859302099/100, 34675228891824302965750984461421798272173/1000)
(3542195259135488956316123763/961, -137192547337235492443922041869661210783152/29791)
(99885604728702440317805311/25, -494380702855584056412453629162798139924/125)
(191274541338903370549182875154887/55338721, -2127659705456508441468528911390514294366655772540/411664745519)
(5738863896025066467592194023/961, -192564760534121725389853705172527183244572/29791)
(7381148914982070467368135, 11966815698759263747168225286133800988)
(3210885514924558403125831, -5814634563264454563489481484708765796)
(4606635579079710636037831, 3400903783661862988545690195227668764)
(83136937226612069792126831/25, -688610853322752322744683721947425186644/125)
(369500271057821897345905409/64, 2968188271461024812060747723350765662533/512)
(148464955644359764950152653207/3249, 56406997530618055317322778110004001373309564/185193)
(442564612968937272308047720823/96721, 102166094462897511960736101897813906171916868/30080231)
(5686849679102777908131415, 5519906177179061213281893610463862348)
(7293822707967841816153543, 11598998806594930087366485213008929308)
(4810144757586570849077483, 3526004198326903889675901133983810328)
(1056038105074123313424501823/196, 12746048661911468363542172355812304723657/2744)
(58730417183209472181144487/9, 229449274691672003141240792136585070996/27)
(491864254513034263853383, 13042591942979503811801652938086444188)
(344102356888558963001132311/81, 2607385123283962563145536817423391657756/729)
(4155878951000322075384263, 3694531535168389481525843863211712028)
(4351216279576288826112415, 3477416178027217992192562309552029348)
(222544528921704313468843125159/289, 104979059589567641727863779517853051897276252/4913)
(4497472803421682296164449543/961, 102091964329769904328649806653229290582628/29791)

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