curve #1264

y² + xy + y = x³ − 16081598888303615150159x + 784937883472625736787999325811122

a-invariants: [1, 0, 1, -16081598888303615150159, 784937883472625736787999325811122]
rank (lower bound): ≥ 7
torsion subgroup: ℤ/6ℤ
conductor (N): 21562908872242620554490
discriminant (Δ): 8166114877639432463036856964198124648037817276784265373786056720
Faltings height: 11.3909
naive height: 165.0095
primes of bad reduction: 2, 3, 5, 7, 13, 17, 23, 43, 47, 59, 199, 4253, 200171
regulator: 633795.1518816153924383957740665848617752755035709031
submitted by: hdeping
submitted at: 2026-09-24 16:47:55 UTC
last updated: 2026-09-24 16:47:55 UTC

(1851340334574/25, 47227468910185208/125)
(2943160734136/9, 4715148081806169970/27)
(72919982379, -84510781248620)
(40024311963523/81, 245582589116776649336/729)
(25947143135167855/239121, 2083766186244555794247232/116930169)
(169560539754689713/576, -69821175766117362705718267/13824)
(34578122648935570824/3575881, -203312941894506192957530381630/6761990971)

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=-952001/50439.

last edited by hdeping at 2026-09-27 08:25:12 UTC · history