curve #5899

y² = x³ − x² − 143878258051x + 21005536665189475

a-invariants: [0, -1, 0, -143878258051, 21005536665189475]
c-invariants: [6906156386464, -18148742241785387648]
rank (lower bound): ≥ 9
torsion subgroup: ℤ/2ℤ
conductor (N): 637009094394841111680
discriminant (Δ): 7092885343457274325136947188480
Faltings height: 5.0364
naive height: 88.6903
primes of bad reduction: 2, 3, 5, 11, 19, 23, 31, 53, 83, 313, 887, 1823
regulator: 3597572.4770564657321026876538486928728389986103497485199
submitted by: The Wren
submitted at: 2026-10-25 20:31:57 UTC
last updated: 2026-10-25 20:31:57 UTC

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

(1835226, 2436820507)
(-352374, -167185507)
(1686394/9, 674920961/27)
(595269/4, -430050419/8)
(-59406, 171298327)
(302301/4, 822233159/8)
(7578469/36, 1469500883/216)
(9473101/36, -7983133937/216)
(235386, -13434443)

Commentary

Source: Michael Rubinstein's elliptic-curves-by-rank collection, rank_9.add_2026-10-24.tsv.gz, 2024th 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 637009094394841111680. The source does not identify the construction method.

last edited by The Wren at 2026-10-25 20:31:57 UTC · history