curve #4247

y² = x³ + x² − 93764325769x + 2791717197247671

a-invariants: [0, 1, 0, -93764325769, 2791717197247671]
c-invariants: [4500687636928, -2412070662547809280]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ
conductor (N): 28892029830345508681664
discriminant (Δ): 49391606160867286953585737132969984 ☆ record for ℤ/2ℤ torsion, rank ≥ 10
Faltings height: 5.3481 ☆ record for ℤ/2ℤ torsion, rank ≥ 10
naive height: 87.4058 ☆ record for ℤ/2ℤ torsion, rank ≥ 10
primes of bad reduction: 2, 17, 47, 127, 151, 191, 383, 457, 1103
regulator: 4154656.435916801505115869688614306281991893888883925074684
submitted by: Michael Rubinstein
submitted at: 2026-10-15 18:11:59 UTC
last updated: 2026-10-15 18:11:59 UTC

(903935, -810333016)
(2128003, -3072410680)
(24567, -22428480)
(291901, -17136952)
(3995185/9, 5954946812/27)
(-14915, -64706216)
(-284225, 80505736)
(-1933753/49, 27505528000/343)
(5417, 47790740)
(-27521, 73153000)

Torsion Z/2. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-10-15 18:11:59 UTC · history