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curve #21

y² = x³ − x² − 852210116x + 9511510378980

a-invariants: [0, -1, 0, -852210116, 9511510378980]
c-invariants: [40906085584, -8217699530925248]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 5131476003533880
discriminant (Δ): 531185208959529592186118400
Faltings height: 3.9568
naive height: 73.3036
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 2179
regulator: 37742.286448328310471088273953984925467953157552812
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:03 UTC
last updated: 2026-07-01 23:00:15 UTC

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

(-10234, 4142592)
(15153, 277620)
(-8324, 4003558)
(54376, 11133058)
(-128603/4, 15339115/8)
(-177656/9, 116575766/27)

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 22:31:53 UTC · history

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