curve #5900

y² = x³ + x² − 94057917670x + 11102259626534904

a-invariants: [0, 1, 0, -94057917670, 11102259626534904]
c-invariants: [4514780048176, -9592379406006446080]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 2817211155038328882208
discriminant (Δ): 7000902337668159546580681059392
Faltings height: 4.9673
naive height: 87.4151
primes of bad reduction: 2, 47, 53, 61, 97, 101, 449, 607, 2237
regulator: 1724620.2415867332848808980581246415543098356379697209492
submitted by: The Wren
submitted at: 2026-10-25 20:43:55 UTC
last updated: 2026-10-25 20:43:55 UTC

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

(132340, 31183948)
(171334, 4066628)
(1681, 104614306)
(197894, 15450988)
(399284, 192882172)
(-1343419/4, 554734561/8)
(192286, 11217856)
(747125/4, 56749559/8)
(180593, 2433190)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2409th data row, added 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 2817211155038328882208. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:43:55 UTC · history