curve #5911

y² = x³ + x² − 7528055510x + 432124066767304

a-invariants: [0, 1, 0, -7528055510, 432124066767304]
c-invariants: [361346664496, -373357361766937600]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 983891285929946218528
discriminant (Δ): -53364684838920136040023239729088
Faltings height: 4.7823
naive height: 80.9226
primes of bad reduction: 2, 11, 31, 43, 47, 97, 167, 311, 463, 617
regulator: 1137665.1730236947623101110730741808587219233578576407772
submitted by: The Wren
submitted at: 2026-10-25 21:12:45 UTC
last updated: 2026-10-25 21:12:45 UTC

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

(84420, 19956248)
(8529, 19197338)
(257958, -125121520)
(-68234/9, 596915416/27)
(-30959, 25209386)
(-1728011/100, 23601909113/1000)
(64676, 14689536)
(-20698, -24063936)
(364942, -215148556)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2119th 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 983891285929946218528. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:12:45 UTC · history