curve #380

y² + xy + y = x³ − 5976631508664466981686244x + 4880007354067700108548264545546534926

a-invariants: [1, 0, 1, -5976631508664466981686244, 4880007354067700108548264545546534926]
c-invariants: [286878312415894415120939689, -4216326353914923211254324408974887585813]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 695690052078788613195618456450521057534158713035141287375452645630
discriminant (Δ): 3375253455561014613462251472724013716887400077887837382135225875155809632100
Faltings height: 13.2182
naive height: 182.7633
primes of bad reduction: 2, 3, 5, 157, 454823, 3225628963, 181698452977764914747, 554098313172672140912966851
regulator: 45273221819276719028.787688152305149482362516246973655696251028597824629923
submitted by: C. R. Hill
submitted at: 2026-08-27 02:20:18 UTC
last updated: 2026-08-27 02:20:18 UTC

Witness: 18 independent points log in to add more points →

(-765919616696, -3001384806186560707)
(11596405929564064/3025, 1029718519147747920935078/166375)
(-762620691224654/289, 7412111953375585848814/4913)
(4898838556213, 9652293418155231293)
(9109015149564566287/2968729, -20091943740108204129586568779/5115120067)
(3983174245470501/49, 251275078931300220092059/343)
(6073277648197233583/3308761, 1843984939993591363018059797/6018636259)
(-1050614784145598/2809, 395661499615016353507126/148877)
(69464002705863695056/30525625, 295188573425844857913002553346/168654078125)
(131543771845963/196, 2969539478909659351177/2744)
(43391344413828386242/1968409, -284130279328111762496878096739/2761677827)
(609136903475220422449/66455104, 14538678343790470032938269519973/541742007808)
(13190206622439193/4096, 1143505507111037828887517/262144)
(5985757895923, 13548828656249720063)
(-21498493221107/16, -207232432563241832143/64)
(6527740523031, 15621208157441614081)
(874985208506803, 25882091378649689235533)
(-2435389291709, 2234020723930872701)

Commentary

Found with Rank Hunter v0.8.0; family=Fermigier--Mestre K3, arithmetic generic rank = 12; parameter=626/3; local status: rigorous rank lower bound >= 18.

last edited by C. R. Hill at 2026-08-27 02:20:18 UTC · history