curve #1830

y² = x³ + x² − 2386801266816420981220x + 44845424005663002738546614573600

a-invariants: [0, 1, 0, -2386801266816420981220, 44845424005663002738546614573600]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/4ℤ
conductor (N): 1185557421935264818440
discriminant (Δ): 1418976757974973134835625339682966206530559094885610057337760000 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7
Faltings height: 11.0399 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7
naive height: 159.2863 ☆ record for ℤ/2ℤ × ℤ/4ℤ torsion, rank ≥ 7
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 23, 31, 67, 89, 193, 347, 2039
regulator: 58861.77373229827689449079238946511408273115528212774
submitted by: dujella
submitted at: 2026-09-25 15:48:59 UTC
last updated: 2026-09-25 15:48:59 UTC

(22032102854, 1718678096630670)
(22764199660, 1519345810983000)
(4756640090, 5796541328047470)
(-26758658452, 9463251767513544)
(-12340124452, 8509977139977456)
(24822560510, 945284011785750)
(14209561490, 3714714049911930)

found by Dujella - Eroshkin (2008)

last edited by dujella at 2026-09-25 15:48:59 UTC · history