curve #1263

y² + xy = x³ − x² − 5786783405422366204704x + 169024703182161975065711634362928

a-invariants: [1, -1, 0, -5786783405422366204704, 169024703182161975065711634362928]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 301672788158929193370
discriminant (Δ): 60038652433835314713547643718527012118714500288254300628906250000
Faltings height: 11.3021
naive height: 161.9432
primes of bad reduction: 2, 3, 5, 7, 13, 19, 47, 61, 73, 83, 2707, 41227
regulator: 311799.8672432902335298920369227112780701058017703416
submitted by: hdeping
submitted at: 2026-09-24 16:47:22 UTC
last updated: 2026-09-24 16:47:22 UTC

(42140817117, -25070715966996)
(41680235457, -488759079516561)
(-1127786291163/16, -963643382304522129/64)
(180918110698185928/305809, -76345461717676353038198692/169112377)
(95979917339304712/962361, -22813154084453910667750036/944076141)
(47598960892, -1192893960666996)
(3520979626682632/121, -208926642899348259701676/1331)

Found by a Mestre-Nagao sieve over the Tate normal form family y^2+txy+(t+2)y=x^3 with torsion Z/6Z, at t=-787299/97525.

last edited by hdeping at 2026-09-27 08:24:25 UTC · history