curve #1498

y² + xy + y = x³ − 999591626088641703x + 349303002842534327752474006

a-invariants

[1, 0, 1, -999591626088641703, 349303002842534327752474006]

rank (lower bound)

≥ 4

torsion subgroup

ℤ/2ℤ × ℤ/6ℤ

conductor (N)

105997974362670

discriminant (Δ)

11212186271858688167710953282838806581275268748075562500 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 4

Faltings height

9.2989 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 4

naive height

135.9520 ☆ record for ℤ/2ℤ × ℤ/6ℤ torsion, rank ≥ 4

primes of bad reduction

2, 3, 5, 13, 17, 19, 29, 31, 37, 41, 617

regulator

639.6659812921650218676012966503389010484293344

submitted by

hdeping

submitted at

2026-09-25 00:42:01 UTC

later contributions

Specialization v=371/617 of the Dujella-Peral torsion Z/2xZ/6 family y^2=x^3+A26(v)x^2+B26(v)x (Contemp. Math. 649, sec 2.2).

last edited by hdeping at 2026-09-27 08:31:02 UTC · history