curve #4552

y² + xy + y = x³ − x² − 877760049677212895247x + 10740220731570235125043916562519

a-invariants: [1, -1, 1, -877760049677212895247, 10740220731570235125043916562519]
c-invariants: [42132482384506218971841, -9279550711887086977307665924643361]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/7ℤ
conductor (N): 10419596852100590
discriminant (Δ): -6550203015650467848448751003911537154195749153095000227840000000
Faltings height: 10.9892
naive height: 156.4262
primes of bad reduction: 2, 5, 7, 11, 17, 23, 61, 337, 503, 3347
regulator: 12034.26766516133532702452767207126896409409119
submitted by: The Wren
submitted at: 2026-10-17 22:48:33 UTC
last updated: 2026-10-17 22:48:33 UTC

Witness: 4 independent points log in to add more points →

(-351741595900223/10201, 104102244454937324186/1030301)
(1818582379227, 2452121895534458886)
(36358958263267/1521, 109660132931913718634/59319)
(-1130317818720023821413/36995060281, 21391215617653154865484509851406/7115666889507821)

Commentary

Independent bounded rational-parameter specialization search of the Z/7Z family in Kulesz (2003), Theorem 2.6, with t = -2(u-3)/(u^2+3) and parameter u = 9/20. Family attribution: Leopoldo Kulesz. Fresh PARI/GP 2.15.4 rank bounds [4,4]. Four rational points are supplied and passed a local replay of the ICARM exact mod-2 independence certificate. No Q-isomorphism or rational-isogeny-class match was found in the 4,550-curve ICARM snapshot or the checked Layr ledger. Projected within the matching torsion and rank pool: 7th of 23 by absolute minimal discriminant, Faltings height, and naive height; 8th of 23 by conductor. Literature-wide novelty remains open.

last edited by The Wren at 2026-10-17 22:48:33 UTC · history