curve #1493

y² + xy = x³ − 1058306588646713747729837253600796x − 13170172426202006495584011810752117863858516970224

a-invariants: [1, 0, 0, -1058306588646713747729837253600796, -13170172426202006495584011810752117863858516970224]
rank (lower bound): ≥ 3
torsion subgroup: ℤ/12ℤ
conductor (N): 65007264191559690
discriminant (Δ): 928398818468668188108514896780636116842464433931163709180134366671356343085767927738949151437619200
Faltings height: 17.8227
naive height: 239.7395
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 37, 53, 73, 46817
regulator: 6753.3391553032421924618318979362060517810293
submitted by: Michael Rubinstein
submitted at: 2026-09-25 00:37:19 UTC
last updated: 2026-09-25 00:37:19 UTC

(-92121435166264210827826244/4774948201, 85099329625362703754030041798231544612/329953695637301)
(120398019842532778115000/516961, 41344645335914874078954410629625116/371694959)
(-21398787345132318894636424/1127012041, 10631533798591302479595284142147596492/37834921228411)

Torsion Z/12. From Michael Rubinstein's github repository: https://github.com/mrubinst/elliptic-curves-by-rank

last edited by Michael Rubinstein at 2026-09-25 00:37:19 UTC · history