curve #683

y² + xy + y = x³ − x² − 398000353985698277x + 14278165486418205635734045

a-invariants: [1, -1, 1, -398000353985698277, 14278165486418205635734045]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 3917124025478839406954796910207131356020026 ★ record for rank ≥ 16
discriminant (Δ): 3946807339033088337040531599824261134462775301725110272
Faltings height: 9.1660
naive height: 133.1893
primes of bad reduction: 2, 3, 7, 19, 233, 165811, 54407921, 778416056663088086001923
regulator: 3427559554894.031139997180134945107127706920508591959724804597559153877
submitted by: 7fff-zip
submitted at: 2026-09-09 00:38:56 UTC
last updated: 2026-09-09 00:38:56 UTC

(-604405409, 5834586305792)
(-438297845, 10223802419060)
(-390052865, 10496681016800)
(-43471889, 5612315322032)
(-30952333, 5154387522220)
(-193537, 3788824884704)
(1710073, 3687486206354)
(35548351, 418110353312)
(639277759, 4593469888160)
(647155615, 5267075860640)
(716520055, 9846724282760)
(755672443, 12042881386304)
(1119607259, 31178353493860)
(1376134201, 45525392306036)
(1469287135, 51003238876064)
(-12991176089/25, 1123475821349344/125)

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