curve #4254

y² = x³ + x² − 4998271918219648433x + 3491313387727359899560711263

a-invariants: [0, 1, 0, -4998271918219648433, 3491313387727359899560711263]
c-invariants: [239917052074543124800, -3016494768435941265667713280000]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 413720850995012265670517042400
discriminant (Δ): 2725943786902164738527872201006837214717748792752064000000
Faltings height: 9.7373
naive height: 140.7805
primes of bad reduction: 2, 3, 5, 7, 13, 23, 31, 37, 47, 61, 101, 109, 409, 1217, 3137
regulator: 625121056.259728222513226232976667522652444198358835680811441
submitted by: The Wren
submitted at: 2026-10-15 19:52:06 UTC
last updated: 2026-10-15 19:52:06 UTC

(-2502449777, 18117933025500)
(-1291443617, 88274547389700)
(-1155803393, 87888091800132)
(-390731273, 73380114686172)
(711558727, 17176228533828)
(717004258, 16617446261325)
(1732856473, 5782069555500)
(2325895423, 66696778757700)
(4237653418, 241679344625775)
(5185263193, 342037853066700)
(3829522594063/1681, 4319387139035814300/68921)

Found in a point-constrained cover search using the X1008 family associated with curve#4118. PARI/GP returned rank bounds [11,11].

last edited by The Wren at 2026-10-15 19:52:06 UTC · history