curve #4153

y² + xy = x³ − x² − 440677961709519413067x + 2788598817413231694706929675841

a-invariants: [1, -1, 0, -440677961709519413067, 2788598817413231694706929675841]
c-invariants: [21152542162056931827225, -2409349378149845744497531046704125]
rank (lower bound): ≥ 17
torsion subgroup: trivial
conductor (N): 6406598481347583107040288514590005345008277552765149950
discriminant (Δ): 2117661086768935173637748366694510079259079843331815533785312500
Faltings height: 10.8641
naive height: 154.2181
primes of bad reduction: 2, 3, 5, 17, 61, 2687, 20530287101, 19897798396246051, 12507442668704146019
regulator: 27526513317919953.2827353053250146371864109614989835272606640544299450632
submitted by: Andrii Prokhorenkov
submitted at: 2026-10-11 17:17:16 UTC
last updated: 2026-10-11 17:17:16 UTC

(-8568833376, 2436298409410913)
(67965106524, 16934725544619763)
(91941247349, -27193229354194462)
(16920443240, 420085526521799)
(17547949178, -677617409368441)
(116528224184, 39163110389252183)
(-3929034576, -2111723403631487)
(-6924646926, 2346936823163363)
(158154382291/9, 18532615233972926/27)
(165019649559, 66511556658431183)
(529774093604/25, 215280378210426607/125)
(7147203578, 63878154336863)
(-2573238189/4, 14021300488864589/8)
(1578176722444/81, -921790708192789973/729)
(-191340658628/9, -43099096123316309/27)
(3285573923906/169, 2752230452523045311/2197)
(-210075335587/16, -160780413217630453/64)

Mestre construction: sextuple [-217, -205, -48, -7, 237, 240], T = 127; 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 17:17:16 UTC · history