curve #3982

y² + xy + y = x³ − 607861530431876339048x + 4127311382934251206939766828006

a-invariants: [1, 0, 1, -607861530431876339048, 4127311382934251206939766828006]
c-invariants: [29177353460730064274281, -3565997034898959072987053635808821]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 498653576436666580377542225670
discriminant (Δ): 7015549784020108327225610128345442751674726764963000531100490000
Faltings height: 10.9578
naive height: 155.1830
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 41, 89, 113, 167, 227, 503, 631, 2063
regulator: 2423260372471450.93289469015255713734843681578657020595578605
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:39:04 UTC
last updated: 2026-10-05 04:39:04 UTC

Witness: 11 independent points log in to add more points →

(12598923324405/529, 21626665150236916709/12167)
(-3245693102498348295/168714121, 6464339917513127323227638723/2191427717669)
(62501386938122841/469225, -15369421269171458287262669/321419125)
(55437023585471209845/7940770321, -334829071522235134461500762863/707609984074631)
(128346319409723745/5424241, 21851043318151224941832703/12633057289)
(-138613035786510/5041, -81133907006623892398/357911)
(726679604591709192141/31529329225, 8601236958710960019703025702719/5598505343837125)
(174542073626332465/25644096, 71755413497308012288956683/129861702144)
(622587055369504416102330/8476174263769, 465453262703439304885884384916828981/24677423561271637603)
(876498632967140977091618/9372127100449, 793704578388751271254394203429098558/28691764300424865457)
(63094502962797783162053250/440158679641681, 494059510260483733835820020691397879058/9234511052376602071079)

Commentary

Unlisted rational-isogeny neighbor of curve#3623 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:39:04 UTC · history