curve #1903

y² + xy = x³ − 3165956472564282588349183356296344123080x + 68556991377202412800271408293265595826883848965311566892352

a-invariants: [1, 0, 0, -3165956472564282588349183356296344123080, 68556991377202412800271408293265595826883848965311566892352]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/8ℤ
conductor (N): 3720844854479034579834388830
discriminant (Δ): 502861743593345625858794128772340004291432295130802525115189867539061671687211124709274546418953109741210937500000000
Faltings height: 21.4085
naive height: 284.4734
primes of bad reduction: 2, 3, 5, 11, 17, 19, 23, 43, 71, 97, 263, 337, 2063, 2957, 9479
regulator: 38359018.069050877826769183558485206186437085344248
submitted by: dujella
submitted at: 2026-09-25 17:50:34 UTC
last updated: 2026-09-25 17:50:34 UTC

(17750661826608305544, 133985647071377314729416784728)
(2437183282546211502906/49, 63372232375562012650626863255454/343)
(21880359321696908904, 98792463770917906389388668888)
(55948597958146717750244594/358801, 394329936946232557094066849818195586572/214921799)
(5608341220821391208742/169, 13821487535430180656025188614452/2197)
(-67529938508386821965888904/2879809, -1761385790564288050226275457245576077456/4887035873)

found by Voznyy (2021)

last edited by dujella at 2026-09-25 17:50:34 UTC · history