curve #4550

y² + xy + y = x³ − x² − 236468853152696217267x + 1399999387817918114106461469459

a-invariants: [1, -1, 1, -236468853152696217267, 1399999387817918114106461469459]
c-invariants: [11350504951329418428801, -1209599471023603978307000326683201]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/7ℤ
conductor (N): 689585803575130
discriminant (Δ): -463165127676081192283014719291202123593980430054850560000000
Faltings height: 10.4241
naive height: 152.3512
primes of bad reduction: 2, 5, 7, 11, 43, 79, 3779, 69763
regulator: 1844.742174502489533361601059984037312637001252
submitted by: The Wren
submitted at: 2026-10-17 22:44:50 UTC
last updated: 2026-10-17 22:44:50 UTC

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

(27230960827, 3892693634521506)
(9467524689, 99176993641568)
(6444935867, 379044761308066)
(2885157584234723/344569, 16977719973528116595398/202262003)

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 = 19/8. 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: 6th of 23 by absolute minimal discriminant and 7th of 23 by conductor, Faltings height, and naive height. Literature-wide novelty remains open.

last edited by The Wren at 2026-10-17 22:44:50 UTC · history