curve #103

y² + xy = x³ − x² − 277442745099x + 47682424180908449

a-invariants: [1, -1, 0, -277442745099, 47682424180908449]
rank (lower bound): ≥ 14
conductor (N): 2373990384245974896168946136843946
naive height: 90.6602
Faltings height: 5.5500
discriminant (Δ): 384586442247847933179369274168719252
primes of bad reduction: 2, 3, 5393, 367261, 66588804478631114025089
regulator: 28502581647696.2529128952344337988779234394456525903918680609725709
submitted by: David Renshaw
last updated: 2026-07-01 22:43:37

(-178921/4, 1959819867/8)
(-2174, 219740875)
(188765, 45039138)
(197344, 24725263)
(442471, 107245690)
(574252, 278511265)
(906415, 735008122)
(1559116, 1844506579)
(2988133/16, 3117289423/64)
(5030386/25, 216919319/125)
(22990075/36, 78094116187/216)
(12142321/25, 20700070241/125)
(5651834483/9604, 279265261887261/941192)
(47714038450/80089, 6936645295043041/22665187)

Found by Zev Klagsbrun.

last edited by David Renshaw at 2026-06-24 02:35:41 · history