curve #2905

y² + xy + y = x³ + x² − 98550613266063337200317355x + 376561777330773011672581883581427255577

a-invariants: [1, 1, 1, -98550613266063337200317355, 376561777330773011672581883581427255577]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/4ℤ
conductor (N): 23959330209511704615223770
discriminant (Δ): 246899560812734106019762632924125764840831090528827445414363867899337113600
Faltings height: 13.5172
naive height: 191.1714
primes of bad reduction: 2, 3, 5, 7, 11, 17, 19, 23, 31, 41, 43, 97, 193, 241, 2087, 2713
regulator: 14149092.41705754057574712136410584021807010042184555
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:27:44 UTC
last updated: 2026-09-26 20:27:44 UTC

Witness: 7 independent points log in to add more points →

(12447532967411643/1849, 339313201431711916360322/79507)
(13780951070733988643/2380849, -859850995256842220824791078/3673650007)
(209423712383438955/17161, 70780925375818346625725106/2248091)
(67282291476523/9, 204955008367285681202/27)
(719845077776728235/121801, -31604987261507925908478258/42508549)
(54699710140459/9, -39145560270981006542/27)
(408196342805737990635/77492809, 1294470641190950171649691248626/682169197627)

Commentary

2-isogenous image of D-z2z4old678-054, rational kernel x=-45905215149213/4. Source: https://dujella.github.io/tors/z2z4old678.html. Independent witness points transported by the degree-2 isogeny. Witnesses saturated by exact rational halves of published and transported relations; quadratic-character independence is certified.

last edited by Natanael Wildner Fraga at 2026-09-26 20:27:44 UTC · history