curve #3093

y² = x³ + x² − 2095665816571588568797400x + 1124962987529349713405567597055502500

a-invariants: [0, 1, 0, -2095665816571588568797400, 1124962987529349713405567597055502500]
rank (lower bound): ≥ 10
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 2065388742404520417852784126936080
discriminant (Δ): 42327704696576286184633156014528686433510195568832546016102906217104000000
Faltings height: 12.8927
naive height: 179.6193
primes of bad reduction: 2, 3, 5, 7, 13, 19, 43, 67, 71, 167, 193, 229, 307, 487, 24847, 887449
regulator: 2681079878.383558765121966238505504015912565186409170300473
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:59 UTC
last updated: 2026-09-26 20:36:59 UTC

Witness: 10 independent points log in to add more points →

(961248978649690/5041, 306276905122607136722160/357911)
(-27974846195/4, 8540235603969152235/8)
(7295460956775, 19342386334530745050)
(5767532982550/121, 1347653238826929852900/1331)
(642688629075, 208720106542837500)
(4296390926841430/961, 268309864661550292745580/29791)
(-411219864331520/361, 9782372921255366841630/6859)
(321470470377887400/458329, 3498396695445412509523950/310288733)
(2686255641325/4, 1144405381680090075/8)
(5368307441672215/5329, 73945254159228534130230/389017)

Commentary

Dujella - Kulesz (2006). Source: https://dujella.github.io/tors/z2z2old1011121314.html (curve entry 84). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:59 UTC · history