curve #3954

y² + xy + y = x³ − 25864822213348529262x − 33515591003346463777169418800

a-invariants: [1, 0, 1, -25864822213348529262, -33515591003346463777169418800]
c-invariants: [1241511466240729404553, 28957470625029077504113283736155]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 19479441722836754745294
discriminant (Δ): 622146694665010005697831715784995712062805234047697654387984
Faltings height: 10.1766
naive height: 145.7118
primes of bad reduction: 2, 3, 13, 17, 29, 83, 179, 373, 863, 5099, 20773
regulator: 671150643.743883984209633493166242965351535003561773099
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:33:34 UTC
last updated: 2026-10-05 04:33:34 UTC

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

(-5630685077386/1369, 2904588261899893737/50653)
(-3281445919, -126585026808651)
(-20796139455922183/6205081, 1925921785320778078334331/15456856771)
(-1302954307940423/553536, 49290940875065540139169/411830784)
(-184870211818/49, -34918143187608981/343)
(-234026302747/121, -128180408590607877/1331)
(-265249184647/121, -149695889544794997/1331)
(4304873183801/121, -8836767881462804661/1331)

Commentary

Unlisted rational-isogeny neighbor of curve#3672 (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 04:33:34 UTC · history