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curve #1259

y² + y = x³ − x² − 16316011147030x + 25367002172345267056

a-invariants: [0, -1, 1, -16316011147030, 25367002172345267056]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 7964090334805
discriminant (Δ): 64815017347270341802028383160753125
Faltings height: 6.0929
naive height: 102.8831
primes of bad reduction: 5, 11, 43, 127, 26515591
regulator: 1179.210443737347533729530916311274875065899855
submitted by: hdeping
submitted at: 2026-09-24 16:31:22 UTC
last updated: 2026-09-24 16:31:22 UTC

Witness: 4 independent points log in to add more points →

(1945060, 995008712)
(22158715, 102683715447)
(18761365/4, 57701881671/8)
(659684035/289, 640308273376/4913)

Commentary

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+(t+1)xy+ty=x^3+tx^2 with torsion Z/5Z, at t=5461/-55.

last edited by hdeping at 2026-09-27 08:29:57 UTC · history

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