curve #3943

y² + xy + y = x³ + x² − 441421609289478350x + 112400512668036984985549067

a-invariants: [1, 1, 1, -441421609289478350, 112400512668036984985549067]
c-invariants: [21188237245894960801, -97114043104095734371726600049]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1906431864891437910
discriminant (Δ): 46955713877915284618309136209582653345733017600000000
Faltings height: 8.9544
naive height: 133.4999
primes of bad reduction: 2, 3, 5, 13, 37, 53, 89, 157, 173, 317, 3253
regulator: 150428755.8222117519301800528286494354996614132234945
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:31:20 UTC
last updated: 2026-10-05 04:31:20 UTC

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

(17786926737, -2370577515863369)
(5337407637, -387053048839469)
(21292787713/49, -557174926485967/343)
(379694840548119649/666414225, -116499600886443891547709887/17203483218375)
(894864998675883697/728514081, -741905626711223769834212999/19663323560271)
(489577310233/9, -342531574083504563/27)
(2094546776833/5184, 32053347593348563/373248)

Commentary

Unlisted rational-isogeny neighbor of curve#3665 (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 04:31:20 UTC · history