curve #4156

y² + xy = x³ − x² − 1779904281852669051x + 913598574571986576331351153

a-invariants: [1, -1, 0, -1779904281852669051, 913598574571986576331351153]
c-invariants: [85435405528928114457, -789349168045737077070110881149]
rank (lower bound): ≥ 16
torsion subgroup: trivial
conductor (N): 911594839462721117866995363316612369336879170828342
discriminant (Δ): 311765435096250622310512414254281430313212676423292964
Faltings height: 9.2172
naive height: 137.6829
primes of bad reduction: 2, 3, 19, 888493995577700894607207956448939931127562544667
regulator: 488160296529835.8724006649863584242892535947383162163860488631586061044
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 17:18:28 UTC
last updated: 2026-10-11 17:18:28 UTC

(799447337, -1264700229550)
(519234368, 11375105555609)
(879336029, -5329157800126)
(1019761172, -12609397295965)
(633944987, -6325737811462)
(74756234, 27945577812467)
(736178096, 1499557442711)
(687813416, 3840530806313)
(-404578369, -39591292743622)
(783615984, -140628874951)
(3014441571/4, 3925325047441/8)
(542751893, -10365395638366)
(809888811, 1815135825883)
(19621442876/25, 39597921938911/125)
(-1311028144, 31523898228791)
(-78831272/9, 823029979540531/27)

Mestre construction: sextuple [-311, -241, -196, -123, 427, 444], T = 13; y^2 = r(x) with p(x-T)p(x+T) = g(x)^2 - r(x).

last edited by Andrii Prokhorenkov at 2026-10-11 17:18:28 UTC · history