curve #5897

y² = x³ + x² − 78318085145x + 8435013668035879

a-invariants: [0, 1, 0, -78318085145, 8435013668035879]
c-invariants: [3759268086976, -7287874364791521280]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 29064479945762992576
discriminant (Δ): 7654400796689968404371928584192
Faltings height: 4.9414
naive height: 86.8657
primes of bad reduction: 2, 23, 41, 73, 113, 353, 1697, 2377
regulator: 237040.31210621284938403478396414971491115837309832245117
submitted by: The Wren
submitted at: 2026-10-25 20:27:12 UTC
last updated: 2026-10-25 20:27:12 UTC

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

(152647, -6071264)
(1742743/9, 621753848/27)
(43489, 71493292)
(542497, 354410036)
(164722, -1945961)
(921951, 848459144)
(206421, 32620256)
(165642, -2653579)
(317511, 124810144)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 1023rd 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 29064479945762992576. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:27:12 UTC · history