curve #3971

y² = x³ − x² − 3872509128953297240x + 2933163095186438831327607600

a-invariants: [0, -1, 0, -3872509128953297240, 2933163095186438831327607600]
c-invariants: [185880438189758267536, -2534252913125800521128503361216]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 188622615993334511234840880
discriminant (Δ): 9876196559540520392216244381899638574382932138496000
Faltings height: 9.2438
naive height: 140.0149
primes of bad reduction: 2, 3, 5, 11, 13, 29, 31, 37, 61, 79, 103, 3299, 6337, 15923
regulator: 192415109330809.3257397840313633543404820650899326979313676
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:36:52 UTC
last updated: 2026-10-05 04:36:52 UTC

Witness: 10 independent points log in to add more points →

(18134083902184473/15904144, -14517904073979007318539/63425726272)
(2573445496900/1849, 1230377942348102080/79507)
(121804996579383540/7059649, 42245451747689327480909280/18757487393)
(1015535620984803788725/760071856041, -7959135043900562930831199056410/662646605605520661)
(8675893191530173377/7628974336, 5813966590237784649809697/666345134403584)
(4781155692333/2209, 7110847638042935046/103823)
(7007862779658504457/6161622016, -14810180822788644611420827/483662681767936)
(2071599777166220481/1821582400, -1232602805642506701955329/77745136832000)
(90041844655222242820/69584636521, 173016402613031620739325863680/18355661683238069)
(176303129516314163031487529332/154999330719300452961, -82281270318745307333176415156533377606368/1929721938985477356083496670959)

Commentary

Unlisted rational-isogeny neighbor of curve#3620 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 10: 10 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 04:36:52 UTC · history