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curve #23

y² = x³ − x² − 1980651076x + 33887665543876

a-invariants: [0, -1, 0, -1980651076, 33887665543876]
c-invariants: [95071251664, -29278372602398912]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 337623153396448920
discriminant (Δ): 1205141092314624597939206400
Faltings height: 4.1000
naive height: 75.8337
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 378343729
regulator: 1652.7003416966787588826095516412822645222470253356
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:04 UTC
last updated: 2026-07-01 23:00:16 UTC

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

(24910, 76704)
(24948, 38246)
(20968, 1255254)
(19074, 1745800)
(10546, 3764640)
(752437/4, 635863443/8)

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 22:31:55 UTC · history

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