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curve #19

y² = x³ − x² − 3272444581x + 72023792282806

a-invariants: [0, -1, 0, -3272444581, 72023792282806]
c-invariants: [157077339904, -62227614068304992]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 4330583892748773660
discriminant (Δ): 1932244778818192209579608400
Faltings height: 4.1886
naive height: 77.3400
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 17614859
regulator: 2971.4872960803653942500626665828891761232773805673
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:02 UTC
last updated: 2026-07-01 23:01:13 UTC

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

(33609, 51175)
(13009, 5626185)
(22653, 3084991)
(61026, 9979340)
(57134, 8459010)
(-216995/4, 75851127/8)

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 22:31:51 UTC · history

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