curve #1086

y² + xy = x³ − x² − 21252276640652798739707819217x + 938627524108684110053910801619511357084941

a-invariants: [1, -1, 0, -21252276640652798739707819217, 938627524108684110053910801619511357084941]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 169865982816721595689011110169981949651950
discriminant (Δ): 233721062158155126934574324579450269809917179389909971086488059245472324281724300250000
Faltings height: 15.2861
naive height: 207.2924
primes of bad reduction: 2, 3, 5, 13, 29, 37, 53, 59, 79, 103, 163, 241, 257, 463, 557, 757, 1481, 2287, 159319
regulator: 117834128118.030247451542313326655324237223950139480060116964
submitted by: dujella
submitted at: 2026-09-23 17:56:38 UTC
last updated: 2026-09-23 17:56:38 UTC

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

(19017299960234, 735761064017992960283)
(139834465497809, 837319973368878505283)
(3252657614678, 932488902903515289863)
(12675419128250, 819318321492432776771)
(44878398411779, 274313029862925460148)
(222075911530490, 2677925266366399108499)
(-48164331466741, -1360329887527677896767)
(257065481913530, 3530293363328357073251)
(46090868872710, 238758440802567342931)
(-163796334743607, -158560586391641489941)
(1768050577343369967/12769, 1163867358320331630990007181/1442897)

Commentary

found by Dujella - Peral (2019), induced by the rational Diophantine triple {21409906185/74591676404, −31580198976/18647919101, −10309975195/18647919101}

last edited by dujella at 2026-09-23 17:56:38 UTC · history