curve #104

y² = x³ − 28776016773697375x + 1902573710284632656267650

a-invariants: [0, 0, 0, -28776016773697375, 1902573710284632656267650]
rank (lower bound): ≥ 16
conductor (N): 48425331144402124316921051447383611482427753400
naive height: 125.3336 ★ record for rank ≥ 16
Faltings height: 8.3191 ★ record for rank ≥ 16
discriminant (Δ): -38740264915521699453536841157906889185942202720000 ★ record for rank ≥ 16
primes of bad reduction: 2, 5, 90031, 533053, 5045220336795543479720942714658869
regulator: 75232573041791.52467258926127736526099781531065272863860954044399433180
submitted by: David Renshaw
last updated: 2026-07-01 22:36:41

(97712665, 154045371730)
(99555245, 156482952370)
(94394865, 165410409770)
(93776785, 169506425930)
(92466365, 179861364770)
(89626805, 208423079030)
(88694525, 219165360670)
(87713925, 231006105670)
(87050045, 239290996130)
(85870605, 254458330030)
(85428185, 260275942930)
(98440675, 154237161920)
(94560695, 164405897120)
(78362825, 358899536830)
(72920105, 438137720030)
(68314345, 505541052130)

Found by Zev Klagsbrun.

last edited by David Renshaw at 2026-06-24 02:36:03 · history