curve #5903

y² = x³ + x² − 353832154289x + 81010807329205231

a-invariants: [0, 1, 0, -353832154289, 81010807329205231]
c-invariants: [16983943405888, -69993439436093754880]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 635502356902517691968
discriminant (Δ): 6084025516032332596392289255424
Faltings height: 5.1865
naive height: 91.3899
primes of bad reduction: 2, 17, 137, 281, 433, 937, 16057
regulator: 2469057.7319090579478456702125370012552720990435133655495
submitted by: The Wren
submitted at: 2026-10-25 20:53:30 UTC
last updated: 2026-10-25 20:53:30 UTC

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

(327082, 16458425)
(1374885/4, 225913/8)
(334371, -9149408)
(3634189/9, 1702234684/27)
(-784661/49, 100980032336/343)
(55806739/169, 29266644304/2197)
(8615739/25, 147826288/125)
(70170, -237755999)
(343003, -316880)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2021st 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 635502356902517691968. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:53:30 UTC · history