curve #5615

y² = x³ − 10527552508545434691

a-invariants: [0, 0, 0, 0, -10527552508545434691]
c-invariants: [0, 9095805367383255573024]
rank (lower bound): ≥ 12
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 111694998055108364588230797740636196
discriminant (Δ): -47878284306318310697474307913119186687792
Faltings height: 6.4847
naive height: 101.1242
primes of bad reduction: 2, 3, 7, 23, 6555427, 52776277
regulator: 864279650522857072.73016545519923832659263193024526740606642878
submitted by: jesper-petersen
submitted at: 2026-10-23 23:08:40 UTC
last updated: 2026-10-23 23:08:40 UTC

Witness: 12 independent points log in to add more points →

(355013472400781707/67271240689, 203811333294734913222106192/17447939883783863)
(7957335971569993/295936, -709825411032179056691131/160989184)
(483792494300255107/130128297289, -300060926146434745460936692/46941571065952837)
(10036542778482319/2804443849, -882496476450029804566330/148514932911493)
(583745883811527075/210994154281, -316275087685746591488879388/96918265821588821)
(612809181177895977/231590012644, -315226496982758519009692917/111449914504773272)
(310647199107412740722439817/288951507122241604, 5475214796315512370897669309595691866683/155323599358751694277045192)
(8048360095768244022961339/2238190924713922369, 20082435237642800239091815505631641560/3348464474728059414067458847)
(177847375478120564161/73041534116356, -1234044545443894477594939269185/624244650584184874504)
(7990035938989026441286191/620932849850055625, -22529290475926979774951293589649197886/489290692581931143356453125)
(11660051634242103734691838713/948332234652371587216, -1255501791773678914595337840722633866709619/29203894394242709784989602883264)
(3181253683356842668243017782360523/365758279698471687768370081, -177989770652624108047890910131525342824292484486956/6995056860845320957076803445366410495729)

Commentary

Exact-rank-12 Mordell curve obtained by the rational 3-isogeny from y^2=x^3+389909352168349433, discovered using the Burkhardt quartic construction with parameters (u,v,w)=(1,3,-3) and specialization t=491/711.

last edited by jesper-petersen at 2026-10-23 23:08:40 UTC · history