curve #5920

y² + xy = x³ − x² − 6104107194x + 157417757709984

a-invariants: [1, -1, 0, -6104107194, 157417757709984]
c-invariants: [292997145321, -136007624174272245]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1154937358986574154706
discriminant (Δ): 3851243032187858623143890731812
Faltings height: 4.5925
naive height: 79.2103
primes of bad reduction: 2, 3, 11, 13, 19, 43, 67, 71, 179, 1873, 344353
regulator: 289461.75055153447813539887355793348190105639108224610583
submitted by: The Wren
submitted at: 2026-10-25 21:35:00 UTC
last updated: 2026-10-25 21:35:00 UTC

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

(84306, 15514344)
(85123, 15913857)
(22233, -5729043)
(-64689, 16812729)
(58390, 236862)
(64755, -5835348)
(-86447, -6207235)
(-68910, -15802938)
(62247, 4286313)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2155th 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 1154937358986574154706. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:35:01 UTC · history