curve #5913

y² + xy = x³ − 19278292183x + 1028309741014032

a-invariants: [1, 0, 0, -19278292183, 1028309741014032]
c-invariants: [925358024785, -888461004273160825]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 1284296073220143470225
discriminant (Δ): 1741625871621898567974716242625
Faltings height: 4.6858
naive height: 82.6603
primes of bad reduction: 5, 19, 61, 229, 241, 971, 3389, 4001
regulator: 1246668.1820857346331161854255802679743887968811418552931
submitted by: The Wren
submitted at: 2026-10-25 21:18:17 UTC
last updated: 2026-10-25 21:18:17 UTC

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

(95741, 7709934)
(373447, 214081419)
(235663/4, 78561697/8)
(36081, -19503975)
(-159632, -6080208)
(65797, 6653534)
(371312, 212096784)
(1328917/16, 15514431/64)
(9392897/64, 18845478035/512)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2190th 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 1284296073220143470225. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:18:17 UTC · history