curve #2225

y² + xy + y = x³ − 22250378827989x + 18605424364010439436

a-invariants: [1, 0, 1, -22250378827989, 18605424364010439436]
rank (lower bound): ≥ 1
torsion subgroup: ℤ/2ℤ × ℤ/6ℤ
conductor (N): 927028830
discriminant (Δ): 555463074754204515458033563316180599272900
Faltings height: 6.7050
naive height: 103.8137
primes of bad reduction: 2, 3, 5, 7, 13, 43, 53, 149
regulator: 4.605816423410060598638804184760271595919
submitted by: Natanael Wildner Fraga
submitted at: 2026-09-26 19:48:14 UTC
last updated: 2026-09-26 19:48:14 UTC

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

(4711223, 4281037788)

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-10, q=53; A=(3q-p)(p+q)^3=13436683, B=-(p+3q)(p-q)^3=37257003. 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 19:48:14 UTC · history