curve #379

y² = x³ + x² − 65188168432120629806876619656x + 6168701434404225366706167935131419820676100

a-invariants: [0, 1, 0, -65188168432120629806876619656, 6168701434404225366706167935131419820676100]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 68282354023300785772619028432224791293185377795283493596007917010323146498247760
naive height: 210.6548
Faltings height: 15.4796
discriminant (Δ): 1290241511271004191707961923166221344342817079498782404272214877293622872824010233676800
primes of bad reduction: 2, 3, 5, 4217, 1668800843, 434121897161, 93127391704528507822425138066232712382500786154827489
regulator: 63155659086251644092.29757316779224019778613109220604430031059120748261
submitted by: Christopher R. Hill
submitted at: 2026-08-27 01:36:07 UTC
last updated: 2026-08-27 01:36:07 UTC

Witness: 16 independent points

(42643705047976, 1861822593558242821314)
(238797775927693966/3025, -204756068733769879759046436/166375)
(8029587091655936185486/42758521, -207244466929221062956033953828204/279597968819)
(1425506870602466968/24649, -6230584840984518637099875990/3869893)
(3164543384461497841093/13380964, -97640985595677382828093341762945/48947566312)
(389627999234101464/49, 243082620369847899916606542/343)
(1509963285868529436037/14092516, 34043600318210567335294432312095/52903305064)
(737872554448006258/2809, 398657546354987882224895280/148877)
(10783717700263113088954/88266025, 138892374250195278556652448691008/829259304875)
(-55606432458312203/196, -3709666914505144816617255/2744)
(9601416973505883444592/22477081, -799351373754977420530017591822630/106563841021)
(98915181169395041900731/194797849, 27725879017144902216344899198170288/2718793578493)
(973553471278024, -29418441614876879456766)
(-2068244305090676384/7921, -1636386961089461615445648594/704969)
(3241023954396001/16, -72282225395532125218041/64)
(21709413616569222616/117649, 26242475189114479645988099538/40353607)

Commentary

Found with Rank Hunter v0.8.5; family=Fermigier--Mestre K3, arithmetic generic rank = 12; parameter=3187/6; local status: rigorous rank lower bound >= 16.

last edited by Christopher R. Hill at 2026-08-27 01:36:07 UTC · history