curve #3939

y² + xy + y = x³ − x² − 189300485590565687220578x + 31727543526925316849311569410180897

a-invariants: [1, -1, 1, -189300485590565687220578, 31727543526925316849311569410180897]
c-invariants: [9086423308347152986587729, -27412597607222584852917633781956650457]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 1693477477526556829770
discriminant (Δ): -721837656470908215502510470839565632841071067029282872684969243485120
Faltings height: 12.1340
naive height: 172.4081
primes of bad reduction: 2, 3, 5, 13, 19, 37, 43, 61, 67, 97, 103, 271, 4327
regulator: 254625068.3629504009668567856281370530687809766246993
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:30:24 UTC
last updated: 2026-10-05 04:30:24 UTC

Witness: 7 independent points log in to add more points →

(-62735041473, 208222056986129215)
(1880606690186989/784, 80296790176689161547373/21952)
(2527315176420147945/31663129, 23316463311692726924379089669/178168426883)
(6843118422691238143/27857284, 1033083481092048085415064805/147030744952)
(3601224276034917/14641, 12119809055254839510415/1771561)
(118642613265825564027/456292321, 90183787242408876581775779965/9746860268881)
(152214093721596524815/5595488809, 68262561723885606296843144968581/418559349379627)

Commentary

Unlisted rational-isogeny neighbor of curve#3719 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:30:24 UTC · history