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curve #1260

y² + y = x³ − x² + 9168180173560x − 714047980228073388

a-invariants: [0, -1, 1, 9168180173560, -714047980228073388]
rank (lower bound): ≥ 4
torsion subgroup: ℤ/5ℤ
conductor (N): 1906325194907
discriminant (Δ): -49540977825774139566862412074262074430123
Faltings height: 6.4981
naive height: 101.1539
primes of bad reduction: 7, 17, 811, 823, 24001
regulator: 3281.582840243524089575598590269726615930777128
submitted by: hdeping
submitted at: 2026-09-24 16:31:56 UTC
last updated: 2026-09-24 16:31:56 UTC

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

(1893569281/81, 83084979357964/729)
(9514885/81, 440148254759/729)
(6637355, 18776144621)
(1282195795491/126025, 1514343655444672511/44738875)

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=5831/-823.

last edited by hdeping at 2026-09-27 08:29:41 UTC · history

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