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curve #20

y² = x³ − x² − 122985156x + 232744673700

a-invariants: [0, -1, 0, -122985156, 232744673700]
c-invariants: [5903287504, -201055978351808]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 26799137200956120
discriminant (Δ): 95659142906961080877830400
Faltings height: 3.6798
naive height: 67.4963
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 107, 467, 601
regulator: 1060.4130531684812274213611098178300928340852385953
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:02 UTC
last updated: 2026-07-01 23:00:15 UTC

Witness: 6 independent points log in to add more points →

(1876, 92862)
(-4892, 846930)
(40616, 7889138)
(10741, 388362)
(13116, 935862)
(311696/25, 99790306/125)

Commentary

Found by Penney - Pomerance (1974). A curve of rank exactly 6, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:52 UTC · history

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