curve #3948

y² = x³ − 475268702023668x + 677242029333930565408

a-invariants: [0, 0, 0, -475268702023668, 677242029333930565408]
c-invariants: [22812897697136064, -585137113344516008512512]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/2ℤ × ℤ/2ℤ
conductor (N): 1012399021707226560
discriminant (Δ): 6672507034577820482606956910530096040040960000
Faltings height: 7.4830
naive height: 112.9983
primes of bad reduction: 2, 3, 5, 11, 29, 61, 101, 163, 443, 2477
regulator: 104294734.2351155906640754701953518685314345650542443
submitted by: Odbayar Shinebayar
submitted at: 2026-10-05 04:32:27 UTC
last updated: 2026-10-05 04:32:27 UTC

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

(-58846431/16, 3119291237425/64)
(-2732395767/196, -185976229713989/2744)
(81199712889/196, -23106367307073875/2744)
(12089401957649/37636, -41938139900829454425/7301384)
(-80626151094504498/4303753609, 15479909450853153298323232/282339148011227)
(-209148324978/17689, -160320106702790672/2352637)
(-1674481475471/129600, -3185280952034189833/46656000)

Commentary

Unlisted rational-isogeny neighbor of curve#3662 (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 04:32:27 UTC · history