curve #1122

y² + xy + y = x³ + x² − 257204508165423954816402995x + 1748673531007907498834205901854033996657

a-invariants: [1, 1, 1, -257204508165423954816402995, 1748673531007907498834205901854033996657]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 429358890253456654402041130
discriminant (Δ): -232025671221059374137572086290042927214552876843271225463270808328445732454400000
Faltings height: 14.1553
naive height: 194.2425
primes of bad reduction: 2, 5, 7, 11, 13, 23, 43, 47, 61, 71, 213061043165881
regulator: 1997859.98878426385139112203482126716223227848708607794
submitted by: dujella
submitted at: 2026-09-23 21:13:57 UTC
last updated: 2026-09-23 21:13:57 UTC

(-2689602117573, -49203604700818714234)
(1495205841187, 36978947192609990766)
(3864476855661, 28503076152165380054)
(6710474255907, 18024565289380447086)
(5067406549627, 23988279478024579006)
(4009191443107, 27963074034705378286)
(-895848773853, -44478881229791043474)
(11572113738915, 17942670234858378606)

found by Dujella - Lecacheux (2009)

last edited by dujella at 2026-09-23 21:13:58 UTC · history