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curve #1254

y² + y = x³ − x² − 18650787970x + 980384795101972

a-invariants: [0, -1, 1, -18650787970, 980384795101972]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 9881581237
discriminant (Δ): 148769899010901018305215717
Faltings height: 4.4089
naive height: 82.5611
primes of bad reduction: 11, 19, 53, 691, 1291
regulator: 253.9346920756941718891937121261882495026971131
submitted by: hdeping
submitted at: 2026-09-24 16:28:35 UTC
last updated: 2026-09-24 16:28:35 UTC

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

(78140, 343491)
(-5612, 32937459)
(144198919/1849, 33190291041/79507)
(477748, 317981900)

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=31217/-341.

last edited by hdeping at 2026-09-27 08:28:05 UTC · history

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