curve #3956

y² + xy + y = x³ − x² − 1911650025077520566x + 846511147475697108683889861

a-invariants: [1, -1, 1, -1911650025077520566, 846511147475697108683889861]
c-invariants: [91759201203720987153, -731385631006085896486136397945]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 830429816548607909946
discriminant (Δ): 137537433657905572676935732566488528096478137409861648384
Faltings height: 9.4913
naive height: 137.8971
primes of bad reduction: 2, 3, 13, 23, 29, 41, 53, 101, 883, 1613, 17021
regulator: 1385191688.54704763857461304655073465784002336102223512
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:33:56 UTC
last updated: 2026-10-05 04:33:56 UTC

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

(-178841415, 34390105909307)
(226531531589/25, -106618502581102173/125)
(490368290337/169, -308591888730042009/2197)
(67777910265/64, -1600262076959321/512)
(-420278159639/1089, 1404216684167139275/35937)
(84786321086665/74529, -244237226109895342661/20346417)
(12403219317177/37249, -112960317620961876789/7189057)
(217259175179085/58081, -3003319986841042101073/13997521)

Commentary

Unlisted rational-isogeny neighbor of curve#3666 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 8: 8 independent points certified by the unchanged ICARM verifier, with a matching unconditional upper bound computed using PARI/GP 2.17.2 ellrank. This is an additional representative of a known isogeny class, not a claim of a new world rank record.

last edited by Odbayar Shinebayar at 2026-10-05 04:33:56 UTC · history