curve #2208

y² + xy = x³ − 60966038780296x + 158104574819660056640

a-invariants: [1, 0, 0, -60966038780296, 158104574819660056640]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 18928364910
discriminant (Δ): 3703805387486079217319327261985991301529600
Faltings height: 6.8928
naive height: 106.8376
primes of bad reduction: 2, 3, 5, 7, 13, 17, 37, 73, 151
regulator: 3.353025275952576208652252703690320283885
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:47:10 UTC
last updated: 2026-09-26 19:47:10 UTC

Witness: 1 independent point log in to add more points →

(5840018, 1110796826)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-17, q=56; A=(3q-p)(p+q)^3=10974015, B=-(p+3q)(p-q)^3=58741567. The listed points are independent modulo torsion by the exact 2-descent Kummer squareclass map. The rank is a proven lower bound; no upper bound is claimed.

last edited by Natanael Wildner Fraga at 2026-09-26 19:47:10 UTC · history