curve #3983

y² + xy = x³ + x² − 1311514981363127632x − 244531530160683403869001040

a-invariants: [1, 1, 0, -1311514981363127632, -244531530160683403869001040]
c-invariants: [62952719105430126361, 211275241586685067652090950915]
rank (lower bound): ≥ 11
torsion subgroup: ℤ/2ℤ
conductor (N): 1758821889262453385218180898874
discriminant (Δ): 118545845533237326614972656669533066216471924208622203152
Faltings height: 9.4536
naive height: 136.7667
primes of bad reduction: 2, 3, 7, 11, 23, 43, 67, 83, 101, 193, 317, 353, 977, 16349, 19867
regulator: 253041255699957.788691526970398351343523233620399095472930895
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:39:22 UTC
last updated: 2026-10-05 04:39:22 UTC

Witness: 11 independent points log in to add more points →

(-276670054616/289, 56797615550477612/4913)
(-22380438345304/34225, 115625022564303204364/6331625)
(-2812560992984/6241, -7872910748678879084/493039)
(17595952442984/361, 73790052943039722596/6859)
(-431366649632024/811801, 12718159546701983174044/731432701)
(-8154937191556/42025, -14051381680239295132/8615125)
(-510426158976071/627264, -8369959618106246150423/496793088)
(-361882761594117976/1346523025, -464902935279309958041524108/49410662402375)
(-3295405887839/3249, -1203684299971941794/185193)
(2694210532611583516/1980517009, -1948664578844911889641048436/88138948451527)
(4653024132746966824/69239041, 10035496754353033477795030412/576138060161)

Commentary

Unlisted rational-isogeny neighbor of curve#3626 (source contributor: Michael Rubinstein). Source equation and witness provenance are credited to that entry. Exact rank 11: 11 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 04:39:22 UTC · history