curve #3824

y² + xy = x³ − 3203533674325860946624870522982915151359635x + 2122926655124747773576345786447252563169067787445714210998440225

a-invariants: [1, 0, 0, -3203533674325860946624870522982915151359635, 2122926655124747773576345786447252563169067787445714210998440225]
rank (lower bound): ≥ 26
torsion subgroup: trivial
conductor (N): 111428230735127928878838361623165208816137759428932113389488903663307468136964829246468164583316055830
discriminant (Δ): 157161965292888291104677464664560768965848284622353591026469655411757049045819654521923011045220924446468272393100122204928000000
Faltings height: 23.3623
naive height: 305.2321
primes of bad reduction: 2, 3, 5, 11, 17, 19, 23, 29, 83, 113, 70508021, 2904627647839522500165918820330960883, 815957259672183188108203906854643580976763963
regulator: 3743119722631803516480755271.01524879690594668489154398855119136372587530896199818085303045
submitted by: 7fff-zip
submitted at: 2026-10-03 05:21:50 UTC
last updated: 2026-10-03 05:21:50 UTC

Witness: 26 independent points log in to add more points →

(1226852817306721901870, 6267514717311263935721482335065)
(-979990432804611584530, 65735793689056257376709881577465)
(1267678467557839896110, 9952201694954325052977802995065)
(60914541187287436136630/49, 2693164295289551721723950078797295/343)
(226261002242320380062, 37545640629804921367158994675481)
(791018507696417449550, -9155361285409457138165155439815)
(1838712247284888957500, 49487208027972739445208500704265)
(856500324572336866820, -2724242963667822271069910176135)
(-1966272596955858408820, -28633705815818112601151193404695)
(-1325454831913461334358, -63564662766575053468008405644699)
(1496984254958079267470, 26114589871626010688932226705465)
(-61144212118291087341055/256, 219602447669998092249637450252483865/4096)
(-584685131925663648130, 61612552555300674614475721185065)
(17613080906657210807516, -2325863214097931069409127388372023)
(11340802419009014958470, -1193472233775223779359784421395535)
(822507633379635208766, 6666156092787456712761116703977)
(71854629917440095172730/169, -63588780701012351676569599382946295/2197)
(-227690732624003127730, 53296692185379841455593945235065)
(863930105647046842670, -336895411470008694569296621735)
(749054335794862587470, 11982782207695125649309635185465)
(3167688022166229333070, 154144402183782055212086021003065)
(5401097942666578130750, 377333267907778346967494892994265)
(1417430106257989874030, -20734316846814818258093232169735)
(1219384285801965940670, -5448681847113696544870973840935)
(-130417014714578124850, 50383566199054194510030785182265)
(855836349304661590670, 2844017741797608797653210750265)

Commentary

X1008; T=-1079/2128; 2-neighbor step: yes (Q has vector q=[-1,-1,-1,1,0,1,0,1,1,1,2,-2,2,1,-1,-1,1] in source section basis; h(Q)=12).

last edited by 7fff-zip at 2026-10-03 05:21:50 UTC · history