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curve #1252

y² + y = x³ − x² − 22323118474870x + 40594673931496079872

a-invariants: [0, -1, 1, -22323118474870, 40594673931496079872]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 2268015996649
discriminant (Δ): 37480426396461743018244819482789186917
Faltings height: 6.3075
naive height: 103.8235
primes of bad reduction: 13, 61, 103, 1061, 26171
regulator: 1699.570862148325288181242748980110494847455987
submitted by: hdeping
submitted at: 2026-09-24 16:27:28 UTC
last updated: 2026-09-24 16:27:28 UTC

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

(9913109/4, 5617221489/8)
(2709023, 42642875)
(104644838387/38809, 638726423948635/7645373)
(241207709/100, 885059039027/1000)

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=18849/-507.

last edited by hdeping at 2026-09-27 08:30:14 UTC · history

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