curve #3945

y² + xy + y = x³ − x² − 16871287805395106x + 513945332552261945881761

a-invariants: [1, -1, 1, -16871287805395106, 513945332552261945881761]
c-invariants: [809821814658965073, -444048763680956155276498905]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 496764009210534318
discriminant (Δ): 193235561581907532217840601098339123129327362084864
Faltings height: 8.3495
naive height: 123.7068
primes of bad reduction: 2, 3, 11, 37, 41, 67, 73, 4523, 74761
regulator: 6014911608.429800512933460634109053048400398439579980
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:31:41 UTC
last updated: 2026-10-05 04:31:41 UTC

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

(166576821093/121, -67690726747844267/1331)
(-9356044990109182455231/76257237386521, 571737375252455353025894579198445/665919299510052706819)
(37159323122465/1151329, -68161352709512762481/1235376017)
(251624476757/16129, 1033428411836537529/2048383)
(10355915361394209/49126081, 865928176187695941294815/344324701729)
(7096992726250561/3448449, -596708867834163692935585/6403769793)
(3480468558382596563140669043187415/2087471514642766101093924, 204716849691250783859691565860480842194147255014251/3015996524993275848361531260807196968)

Commentary

Unlisted rational-isogeny neighbor of curve#3660 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 7: 7 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 04:31:41 UTC · history