curve #1835

y² = x³ + x² − 126805284556646749335939083075808898286800006041x + 6437933136993997783664151467830511224300392764380156814845149031129959

a-invariants: [0, 1, 0, -126805284556646749335939083075808898286800006041, 6437933136993997783664151467830511224300392764380156814845149031129959]
rank (lower bound): ≥ 14
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 484189562005603156918334765670379702209992995855025668493778467960640 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 14
discriminant (Δ): 112589350781942194888579491033184178414092081975054671003065033975490720627380837071088303353784342765037086191441429519472768439249967321190400 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 14
Faltings height: 26.1419 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 14
naive height: 336.9905 ☆ record for ℤ/2ℤ × ℤ/2ℤ torsion, rank ≥ 14
primes of bad reduction: 2, 3, 5, 7, 11, 19, 31, 41, 59, 61, 67, 89, 107, 137, 173, 199, 241, 263, 347, 383, 421, 607, 613, 821, 1103, 1621, 4127, 6491, 21319, 22639
regulator: 1223461022305635.53962553375166640654571610371008226276715870721884
submitted by: dujella
submitted at: 2026-09-25 16:28:11 UTC
last updated: 2026-09-25 16:28:11 UTC

(-81970142887190856673101, 127598646111012566660826968605543800)
(-189841345734961210155471, 153847284398716351048583584847780100)
(-169978767562208206585641, 151924256617426548755962219254153720)
(330146201149265817802419, 23631234300896247709645396196927880)
(33932177644287702305715, 46628563736499124960967519990139912)
(5040642034464253787296671, 11288943893314536628860892480063576320)
(870039962976637951825425, 744785886114577052424857904897681972)
(-94766107666974777578601, 132679005282070753002699166761858600)
(36383241902220788682821, 43272482685006943024094711026446000)
(327328151981619918488919, 1466030136187066302988802308829880)
(-351953105333062185489054, 86433024924668666503453219833567375)
(8755000490564937382613510769/64, 819186508720383208130501627010616119714345/512)
(-214921905990474863361741, 154154524218964374569895225646078920)
(-306381817107001718214441, 128564230144636012650749795989468680)

found by Elkies (2005)

last edited by dujella at 2026-09-25 16:28:11 UTC · history