curve #3042

y² + y = x³ + x² − 1805632198953220354072743054330x + 937164323059943920996847199260009653476285734

a-invariants: [0, 1, 1, -1805632198953220354072743054330, 937164323059943920996847199260009653476285734]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 1081272252106752146999637106755
discriminant (Δ): -2652997589211787107549609960763935271906042933101162278505560435058165717701520446152996875
Faltings height: 16.2068
naive height: 220.6260
primes of bad reduction: 3, 5, 7, 13, 17, 29, 31, 37, 41, 43, 59, 434431, 31000374311
regulator: 4006404.58857809070596279583881531983251471294729208522
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:36 UTC
last updated: 2026-09-26 20:34:36 UTC

Witness: 8 independent points log in to add more points →

(494276905555896, 12862295658942711715597)
(737119316569371, 2589973408237602569227)
(826315889039376, 3057538411111718341762)
(-233877846248124, 36696986856509114936362)
(508285609696236, 12276205155103716481882)
(-67908599195559, 32549487101362118890957)
(575624023395156, 9408934695207694614922)
(-348343747461429, 39036851906891076445252)

Commentary

Dujella - Lecacheux (2009). Source: https://dujella.github.io/tors/z5old678.html (curve entry 4). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:36 UTC · history