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curve #14

y² = x³ − x² − 24649x + 1355209

a-invariants: [0, -1, 0, -24649, 1355209]
rank (lower bound): ≥ 4
conductor (N): 13217088
naive height: 41.9511
Faltings height: 1.4676
discriminant (Δ): 174691415199744
primes of bad reduction: 2, 3, 23, 41, 73
regulator: 24.11485382784266345603218697563936280642992865
submitted by: David Renshaw
last updated: 2026-07-01 23:03:10

Witness: 4 independent points

(40, 657)
(21, 920)
(-55/16, 76797/64)
(3305/121, 1114848/1331)

Commentary

Found by Wiman (1945). A curve of rank exactly 4, via Dujella's elliptic-curve rank-records tables.

last edited by David Renshaw at 2026-05-27 22:31:46 · history

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