curve #5902

y² + xy = x³ + x² − 20236429168x + 1101562567699372

a-invariants: [1, 1, 0, -20236429168, 1101562567699372]
c-invariants: [971348600089, -951757343606758013]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 2393546772234518311830
discriminant (Δ): 6159113018610492328710227108100
Faltings height: 4.7427
naive height: 82.8059
primes of bad reduction: 2, 3, 5, 31, 61, 67, 677, 3769, 8161, 30241
regulator: 511835.10841135374717707224773001666338824037365060226700
submitted by: The Wren
submitted at: 2026-10-25 20:51:22 UTC
last updated: 2026-10-25 20:51:22 UTC

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

(-17739, 38152742)
(-160586, 14575540)
(58831, 10678372)
(-119289, 42698797)
(90581, -3472603)
(66886, 6841492)
(66209, 7175930)
(285823/4, -36425437/8)
(1367403, -1591340899)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2354th 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 2393546772234518311830. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:51:22 UTC · history