curve #5907

y² = x³ + x² − 47164230545x + 3942260054268559

a-invariants: [0, 1, 0, -47164230545, 3942260054268559]
c-invariants: [2263883066176, -3406126270186432000]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 74259467769292508224
discriminant (Δ): 625906662606597087417013256192
Faltings height: 4.7843
naive height: 85.3443
primes of bad reduction: 2, 17, 47, 89, 463, 1657, 14057
regulator: 505749.91446918363993037159621018090924717615404479084525
submitted by: The Wren
submitted at: 2026-10-25 21:05:22 UTC
last updated: 2026-10-25 21:05:22 UTC

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

(113979, 6875072)
(122379, -1785328)
(43669, -44338732)
(1150489/9, -38977192/27)
(124481, -350304)
(63115, -34884272)
(496461/4, -5186989/8)
(129787, -2681696)
(252019, 89792368)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1467th 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 74259467769292508224. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 21:05:22 UTC · history