curve #3080

y² + y = x³ + 87299817093221362429969788356520

a-invariants: [0, 0, 1, 0, 87299817093221362429969788356520]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/3ℤ
conductor (N): 9428380246067907142436737142504187
discriminant (Δ): -3292383483868278860615936775487253728617635387261104834928937501147
Faltings height: 11.4424
naive height: 160.6169
primes of bad reduction: 3, 13, 23, 31, 43, 61, 73, 157, 199, 337
regulator: 736237929.26318997057405429927313082439417920105472609687
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 20:36:19 UTC
last updated: 2026-09-26 20:36:19 UTC

Witness: 9 independent points log in to add more points →

(-34739896854, 6735993625205487)
(59816792760, 17358779174601879)
(-44207258970, 952038792981504)
(6576595440, 9358646559113879)
(55473407808, 16062629859888488)
(-19255568904, 8953228261141352)
(101583478425/4, 81458264395412407/8)
(11986370039488/81, 42053694778844172287/729)
(-2123513196948/49, 833762857240311704/343)

Commentary

Elkies - Rogers (2004). Source: https://dujella.github.io/tors/z3old891011121314.html (curve entry 51). Published independent points; exact point coordinates checked.

last edited by Natanael Wildner Fraga at 2026-09-26 20:36:19 UTC · history