curve #5935

y² = x³ − x² − 2552887091x + 49647933159420

a-invariants: [0, -1, 0, -2552887091, 49647933159420]
c-invariants: [122538580384, -42895079018256608]
rank (lower bound): ≥ 8
torsion subgroup: ℤ/2ℤ
conductor (N): 518968062402309960
discriminant (Δ): 8801354781485866592406480
Faltings height: 3.9876
naive height: 76.5951
primes of bad reduction: 2, 3, 5, 11, 37, 59, 67, 181, 317, 4259
regulator: 284383.128476706348208916817217854576403233862264513664
submitted by: The Wren
submitted at: 2026-10-25 22:36:27 UTC
last updated: 2026-10-25 22:36:27 UTC

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

(76069, 17193583)
(-507899/9, 100985149/27)
(78549/4, 21299259/8)
(465529/16, 1108987/64)
(121405/4, -2808215/8)
(117061/4, -189869/8)
(103415449/3249, -147809110339/185193)
(8508889, 24819991163)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz, 484255th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/torsion/torsion_Z2.add_2026-10-24.part3.tsv.gz The source lists proven rank 8 and torsion Z/2. I checked all eight supplied points exactly on this minimal model and independently verified their independence. The full torsion group and supplied torsion generator were checked separately. Conductor 518968062402309960. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 22:36:27 UTC · history