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curve #25

y² = x³ − x² − 3002115396x + 63280268148996

a-invariants: [0, -1, 0, -3002115396, 63280268148996]
c-invariants: [144101539024, -54673287071498432]
rank (lower bound): ≥ 6
torsion subgroup: ℤ/2ℤ
conductor (N): 508534208459997720
discriminant (Δ): 1815205696936306744772102400
Faltings height: 4.1738
naive height: 77.0814
primes of bad reduction: 2, 3, 5, 7, 11, 13, 17, 19, 23, 83, 409, 16787
regulator: 2425.4713982456645308215970211688915508648574748522
submitted by: David Renshaw
submitted at: 2026-05-27 22:12:06 UTC
last updated: 2026-07-01 23:01:13 UTC

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

(32273, 76076)
(24196, 2192250)
(-45490, 10281544)
(62528, 10955774)
(127164, 41687310)
(350114, 204765680)

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 22:31:57 UTC · history

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