curve #5446

y² = x³ + 2379977897209563780879854107127158972

a-invariants: [0, 0, 0, 0, 2379977897209563780879854107127158972]
c-invariants: [0, -2056300903189063106680193948557865351808]
rank (lower bound): ≥ 17
torsion subgroup: trivial
family: y² = x³ + k (Mordell curves)
conductor (N): 166700957528570161370331561792365459958429300339280355086852540995984
discriminant (Δ): -2446975349801016598967986779847751469332510683557839333220253858053161810688
Faltings height: 13.1446
naive height: 181.0435
primes of bad reduction: 2, 3, 7, 79, 3323, 7021367, 2626924397, 31744104551
regulator: 19807403485655851082.2396796436438942939620264697470154372017065539012964
submitted by: wgxli
submitted at: 2026-10-22 03:58:26 UTC
last updated: 2026-10-22 03:58:26 UTC

Witness: 17 independent points log in to add more points →

(294129787098, 1550942858683573642)
(769177761458, 1683760654812637122)
(-1188339507886, 837772837414915746)
(1068003335714, 1896885801420726354)
(1334438564837, 2180882326742155365)
(1574918905413, 2507261216447653813)
(2407394001173, 4041304278910758867)
(2729617098509, 4766322997694511351)
(3316268230898, 6233063884956835458)
(68669583428138, 569047101088034101638)
(-4913070098223/4, 5807377450270000871/8)
(444422566948962, 9369019894058773390610)
(-11349374372727/16, 91030192042262842277/64)
(5318002887386/25, 193229278077384358866/125)
(5474617520682/49, 529307190375226164586/343)
(-161469292321799/144, 1701967939064888895757/1728)
(-15792559964722303/29584, 7595022470777411140098369/5088448)

Commentary

Mordell curve y^2 = x^3 + 2379977897209563780879854107127158972, submitted by wgxli: https://elliptic-rank.icarm.cloud/curve/5446 The 17 submitted points are the exact witness points recorded on the source curve. ICARM records rank lower bound ≥17, trivial rational torsion, conductor 166700957528570161370331561792365459958429300339280355086852540995984, and minimal discriminant -2446975349801016598967986779847751469332510683557839333220253858053161810688. The source record contains no method commentary or transformation, so none is added here.

last edited by The Wren at 2026-10-22 13:25:27 UTC · history