curve #3957

y² + xy = x³ − 261274505197258155628943019373106528270x + 1169760029681562714070019912702978627750639550628567056900

a-invariants: [1, 0, 0, -261274505197258155628943019373106528270, 1169760029681562714070019912702978627750639550628567056900]
c-invariants: [12541176249468391470189264929909113356961, -1010672665644870184975308968949576121581836469137945607197041]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/6ℤ
conductor (N): 11562784654375022501788319763332764230
discriminant (Δ): 550365034897143495624094836456818932672813714435075450998615205649043737983621940843228783877808784024137781328192000
Faltings height: 21.1076
naive height: 276.9895
primes of bad reduction: 2, 3, 5, 7, 11, 13, 19, 23, 29, 37, 43, 67, 113, 419, 421, 677, 4639, 52081, 87421
regulator: 255249094490.37602848390761482171712973327985715038968984
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:34:06 UTC
last updated: 2026-10-05 04:34:06 UTC

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

(24886090592368449580, 100399454956338682280050118290)
(189317464585511304165911624560/3951505321, 78007522417132566931229801603987384222545130/248395575983381)
(313986353115953192721113380/6046681, 5311710376202265530334920914686939163310/14868788579)
(2190678091046096831371534/162409, -653506634721959829747958512211966796/65450827)
(1647063672086135566748050/961, 2113714457871121122511792899854368120/29791)
(60396081551009096679268/4489, -2852502756641914790200162840581794/300763)
(2320297182422620021630/49, 105707234115983425107242438874250/343)
(80958606286245429715840296/801025, 719482887277826439307083078684555381834/716917375)
(569378578337821202394930055/42276004, 2663221300662040818179259246980352256975/274878578008)

Commentary

Unlisted rational-isogeny neighbor of curve#3834 (source contributor: dujella). Source equation and witness provenance are credited to that entry. Exact rank 9: 9 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 04:34:06 UTC · history