curve #1877

y² + xy + y = x³ − x² − 221613919436417279191008545468564120651958897x + 1329680042545478090107165280489237396683959793078313785673106433569

a-invariants: [1, -1, 1, -221613919436417279191008545468564120651958897, 1329680042545478090107165280489237396683959793078313785673106433569]
rank (lower bound): ≥ 24
torsion subgroup: trivial
conductor (N): 14652708046031414428807315213016786537371791158212267657970049507436499202465230555912830
discriminant (Δ): -67217051084373242823120114806453966902840141761823124851922296702490979342660452591814029607945139821478107635687291035580653568000000
Faltings height: 24.4366
naive height: 318.0343
primes of bad reduction: 2, 5, 7, 11, 13, 17, 19, 23, 31, 53, 67, 73, 79, 139, 157, 14222524493833307911009625497484357655533225908602900366819622852087
regulator: 249962616033640960634603.22264286415138921230293189433708846609231660719374628522136856
submitted by: Ritik Jain
submitted at: 2026-09-25 17:28:11 UTC
last updated: 2026-09-25 17:28:11 UTC

Witness: 24 independent points log in to add more points →

(8134086568577897838087200295974654514377815714657604767/445772666864308395463889679528121, 17255636151060712870238754768204891860077429461680397087350815143266247750264346116/9411745031741355129508235039768406202047876369581)
(7658240395759665755127, -285749544354432300837099550736364)
(236038764011088994151997703/1089, -3618068047809509761600647654548154004268/35937)
(-8016848934723848631979494137/471969, -142506271291583194035417696912714954649492/324242703)
(-55333766239436255028693977/3249, 75009162714608877168291703992268928948/185193)
(80431882839725959158360740983/21372129, -73205204905386793501415678009168560522002388/98803352367)
(6528979072520582939564863/729, 4950867443270411458938178593669824828/19683)
(193648589868498991945187, 84971720408345453131554224784535636)
(-1098522473554417263616313/81, -989072390096040403798047196976994956/729)
(51145641121063362800087, 11125905812219493515784333085904276)
(13189616605749241901139673/1024, -25637615470782347467955599776697840627/32768)
(9540036770659374345527, 289371397926051399816962105549236)
(332087147489162523927, -1120768277294248233696018939494764)
(483988767793409412694919563/45369, -4094984450249856339373630834682598606908/9663597)
(7321707784015192904727, 315571603776352827130044431846036)
(35822413874092271363933783/529, 209628717964740005945387286812276254412/12167)
(3750293503285384220524447/361, 2643992635145079832884158226695808924/6859)
(38802631404558677468687/4, 2436232360344505738525992861836579/8)
(-30434035826941760037617287347501271623493880673/1816966776543972664217161, 1433021003702066149553944587564964617618255510424372269307497496786796/2449178731410371710883384793517548091)
(1125929781332451530850933936141927748459658807/27724243799754509823841, 35551451608946000949785072446520610556878525034792174624160398477804/4616252585441819036051350076918639)
(-33813986637028951602293035872818619279471678050893857/1966303003048532911366621761769, 647611481761117821099317816917560368147577533569084821936347981015226827416692/2757246942093029663048104516061590073454273397)
(908368479255310140286139777004673947559920727/88411960485459461024001, 9741574092561553467468775428446624166747452729459414636896046265964/26288543887655306544069001592463999)
(-397522499601117310568146781946516044476320554093047153/74300813629754549495542162587841, 984349752666701331188151694250974766567557473190918877810093642491855234966554956/640457556792274831609514494721298061028454566111)
(-9177962403725262376838458497/543169, 200161624901096965411306805481422411870028/400315553)

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