curve #5555

y² + xy + y = x³ − 641349695536644061456326644203x + 211633246110324080333245434738455994980803298

a-invariants: [1, 0, 1, -641349695536644061456326644203, 211633246110324080333245434738455994980803298]
c-invariants: [30784785385758914949903678921721, -182851124639320051585102134252398404518932432269]
rank (lower bound): ≥ 18
torsion subgroup: trivial
conductor (N): 1458142874004286384264242840405732560735763666699062430
discriminant (Δ): -2465104149988738038790015820884628588173854782065525713745503258589373060246800792860937500
Faltings height: 16.0896
naive height: 217.6500
primes of bad reduction: 2, 3, 5, 11, 13, 23, 37, 43, 47, 53, 139, 176903, 151642538601742708809473420116543777
regulator: 1741204652140932.5530921255804084688481465693968375806126380305213276724368
submitted by: apkorte
submitted at: 2026-10-23 02:38:05 UTC
last updated: 2026-10-23 02:38:05 UTC

Witness: 18 independent points log in to add more points →

(552883629353224, -5103639825713776866175)
(558084612376174, 5246523294531090456800)
(520258894159459, -4333991753115983958370)
(428868509428099, 3931865811257613120950)
(16431148059805141/9, 1933085097847038566909900/27)
(332639868813124, -5924620852929634571350)
(-810634211046491, -14101168173747640619290)
(-291552619626671, -19334880330195092076070)
(2454455148128791/4, 56074945725457883256265/8)
(1212618477339724, 34885638267826828016450)
(-578107151422151, 19728003913984773344450)
(5544016134175974, -408726680481863806491800)
(454892278099054, -3744023398864316818720)
(383675891128699, -4694963422428134291950)
(2712927113129974, 135789431168874686202200)
(8292549277710724, 751759099811056170743825)
(768488797347349, 13138244769622701487700)
(455661823205524, -3742017003666401122150)

Commentary

Specialization at T = 45/32 of the rank-17 fibration of X1152 given in curve#3926. Found by Claude (Anthropic): a Mestre-Nagao sieve over the fibration, then a 2-covering point search seeded with its generic sections.

last edited by apkorte at 2026-10-23 02:38:05 UTC · history