curve #3980

y² + xy = x³ − 906339880423424372439x + 10365657026340653561180994760809

a-invariants: [1, 0, 0, -906339880423424372439, 10365657026340653561180994760809]
c-invariants: [43504314260324369877073, -8955927670823581148250866028154585]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 2355694911715481929719037783146
discriminant (Δ): 1231902755398768614905909874098026645590549247494009314159038464
Faltings height: 10.9085
naive height: 156.3814
primes of bad reduction: 2, 3, 11, 31, 37, 41, 127, 271, 293, 397, 577, 823, 1483, 24473
regulator: 54923419071719.6065831789499234670895188599567083927447542468
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:38:43 UTC
last updated: 2026-10-05 04:38:43 UTC

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

(7553256825606, -20758597694177986443)
(92268793743/4, 10531053018043977/8)
(29732181945846/841, 115713154662307060233/24389)
(220295726476998/3481, 2951067868374747480159/205379)
(1454018634140379414/7491169, -1733335966159122922328013339/20503329553)
(95455170308346486/4036081, -11914469584303961592804867/8108486729)
(9176861012838/361, -13287778652049106521/6859)
(6606821557806/25, -16876266399246081111/125)
(536018921754/25, -111067886055970743/125)
(540698846581482/25921, -3056001765083622926691/4173281)
(8591599036544136/429025, -139520557589277359296749/281011375)

Commentary

Unlisted rational-isogeny neighbor of curve#3627 (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 04:38:43 UTC · history