curve #1917

y² + y = x³ + x² − 43404903968582650644659510x + 110583089765290602424908396450544942556

a-invariants: [0, 1, 1, -43404903968582650644659510, 110583089765290602424908396450544942556]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 83898344850864966640886745
discriminant (Δ): -49213783699449795109892645007552064905763846828414326376048556415922904146875 ☆ record for ℤ/5ℤ torsion, rank ≥ 8
Faltings height: 13.5597 ☆ record for ℤ/5ℤ torsion, rank ≥ 8
naive height: 188.7208 ☆ record for ℤ/5ℤ torsion, rank ≥ 8
primes of bad reduction: 3, 5, 7, 11, 19, 23, 29, 31, 41, 67, 1718791, 39160529
regulator: 758219.459965725240632589282849323584788009151270904664
submitted by: dujella
submitted at: 2026-09-25 18:51:31 UTC
last updated: 2026-09-25 18:51:31 UTC

(2951970089353, 2859537547106976928)
(2321311057630, 4726008474709220212)
(3043048878055, 2584361387394463462)
(2704356610900, 3602663413910274532)
(4945869383740, 4110000139693492852)
(1220815771180, 7707995295248643412)
(6757908401914, 11219886194838910627)
(2991001241590, 2741665496971153252)

found by Klagsbrun (2020)

last edited by dujella at 2026-09-25 18:51:31 UTC · history