curve #3031

y² + xy = x³ − 26585801149299063128485194924055x + 59129117530968104964891765336439392682133478377

a-invariants: [1, 0, 0, -26585801149299063128485194924055, 59129117530968104964891765336439392682133478377]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/5ℤ
conductor (N): 31153924504241335438249182010590
discriminant (Δ): -307758859260195276257477720931541175647911186499591380895767800007769418255466836139325132800000
Faltings height: 17.0524
naive height: 228.9153
primes of bad reduction: 2, 3, 5, 7, 11, 17, 23, 29, 43, 61, 73, 89, 1621, 3221, 13367221081
regulator: 4311249.46996155247873135318290581518572415613195342010
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:34:07 UTC
last updated: 2026-09-26 20:34:07 UTC

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

(2808024629488862, 81343798769469590888285)
(746810157817034, 199226218236964284070973)
(-57352132147846, -246279680954672328841687)
(2352360567963794, 98014029692395964532653)
(1034557970875894, 180919492582532234439253)
(608050697885942, 207818224422580788241493)
(1319099844527468, 162342406873363171316591)
(-5814632461591786, -130856190140250291639787)

Commentary

Dujella - Lecacheux - Petricevic (2021). Source: https://dujella.github.io/tors/z5old678.html (curve entry 9). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:34:07 UTC · history