curve #1719

y² + xy + y = x³ + x² − 18339149952021972205x + 30228255651982426022119325475

a-invariants: [1, 1, 1, -18339149952021972205, 30228255651982426022119325475]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/5ℤ
conductor (N): 999640295425114970
discriminant (Δ): 6961091434246078275355128262815537187826271040000000000
Faltings height: 9.6816
naive height: 144.6803
primes of bad reduction: 2, 5, 11, 17, 19, 23, 47, 389, 6599, 10139
regulator: 9348.0443724085490213696471186041550472104021140984
submitted by: Michael Rubinstein
submitted at: 2026-09-25 06:15:27 UTC
last updated: 2026-09-25 06:15:27 UTC

(22197634687/9, 1902250750556/27)
(-4672086357, 118011744661928)
(14172356843, 1617681978960428)
(129631122583/81, 51431494926913012/729)
(19097128343, 2577728180666228)
(2465098643, 365955714428)

Torsion Z/5. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 06:15:28 UTC · history