curve #3949

y² + xy = x³ + 58777292179154167330261654x + 1191616953756549805868821004651060172196

a-invariants: [1, 0, 0, 58777292179154167330261654, 1191616953756549805868821004651060172196]
c-invariants: [-2821310024599400031852559391, -1029557048045654800305624448918468209938257]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/6ℤ
conductor (N): 31566406933966762584842830
discriminant (Δ): -626414786585853603408468118439385341122779965485497313373089295914995933868195840
Faltings height: 14.1836
naive height: 193.4754
primes of bad reduction: 2, 5, 11, 13, 19, 37, 61, 73, 181, 223, 307, 317, 787, 2281
regulator: 9573157716.14154920075581948639462994360303070162878758
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:32:37 UTC
last updated: 2026-10-05 04:32:37 UTC

Witness: 8 independent points log in to add more points →

(10798964783028, 55549077884036371270)
(-2532103995272172/841, 766356387598490901019870/24389)
(407724103046382420/67081, -731651695983946010481057886/17373979)
(1650341559380152/9, 67109170994051133619190/27)
(-354783418845403308/120409, 1316528334941854602676828306/41781923)
(-4835488527740218248/552049, -893727691063318172691777106/410172407)
(1575885813559474797396/41434969, 64477707423990244296455505296494/266716895453)
(236965581584207538360/6713281, 3780806718237665813689914911294/17394111071)

Commentary

Unlisted rational-isogeny neighbor of curve#3843 (source contributor: dujella). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 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 04:32:38 UTC · history