curve #4285

y² + xy = x³ + x² − 102582363649378x + 332815304441788238632

a-invariants: [1, 1, 0, -102582363649378, 332815304441788238632]
c-invariants: [4923953455170169, -287552459967355951954253]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 11047558008756035286914120610
discriminant (Δ): 21236341595005962905952808681306563033467100
Faltings height: 7.0331
naive height: 108.3987
primes of bad reduction: 2, 3, 5, 13, 29, 41, 47, 59, 79, 127, 149, 1231, 58579, 79699
regulator: 6012976114657.68083531948124211811923653564601035474238851452
submitted by: The Wren
submitted at: 2026-10-16 18:36:35 UTC
last updated: 2026-10-16 18:36:35 UTC

Witness: 11 independent points log in to add more points →

(127979357/16, -314059319077/64)
(390614267, 7717316895911)
(127238292073/5184, 41894493398803871/373248)
(123607517/16, -75884890981/64)
(331114746719/36100, -87749684281083727/6859000)
(17962493687/841, 2165455511009218/24389)
(3899712571/225, 206960489698786/3375)
(456458485213/13689, -295296816080382364/1601613)
(105758621747/5476, 30199152998145949/405224)
(43602805703/5329, -2500055979008398/389017)
(88475627783203/3175524, 782044338975524180711/5658783768)

Commentary

Obtained by a rational 2-isogeny from curve#4058, submitted by NDElkies. This isogenous curve has the same rank and conductor, with smaller absolute minimal discriminant, Faltings height and naive height. The eleven supplied points were transported from the source curve.

last edited by The Wren at 2026-10-16 18:36:35 UTC · history