curve #5914

y² + xy = x³ + x² − 9783771727x + 348114773405425

a-invariants: [1, 1, 0, -9783771727, 348114773405425]
c-invariants: [469621042921, -300774686380109045]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1741699448364808943094
discriminant (Δ): 7584870144798490876778897849412
Faltings height: 4.6715
naive height: 80.6256
primes of bad reduction: 2, 3, 7, 41, 43, 103, 337, 571, 7753, 153073
regulator: 464917.33822505442995612904368864952487896506546249221685
submitted by: The Wren
submitted at: 2026-10-25 21:20:43 UTC
last updated: 2026-10-25 21:20:43 UTC

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

(-103221, 16121549)
(-1583, 19069051)
(44668, 445315)
(31627, 8369896)
(43968, 1693415)
(44097, 1537067)
(92061, -15134420)
(-241013/4, 214736021/8)
(-5009, 19927264)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2260th data row, added on 24 October 2026: https://github.com/mrubinst/elliptic-curves-by-rank/blob/5e2e867ddb468765263bfadf520d9acda17a5a4b/rank_9.add_2026-10-24.tsv.gz The source lists proven rank 9 and torsion Z/2. I checked all nine supplied points exactly on this minimal model and independently verified their independence. The full torsion group was computed separately. Conductor 1741699448364808943094. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:20:43 UTC · history