Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #2247

y2 + xy = x3 − 12360706320466x + 11055717559828669700
a-invariants
[1, 0, 0, -12360706320466, 11055717559828669700]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
2970167970
discriminant (Δ)
68064692543842710602838057931886926233600
Faltings height
6.5383
naive height
102.0502
primes of bad reduction
2, 3, 5, 7, 11, 19, 31, 37, 59
regulator
3.967895509660914605405678288860490177341
submitted by
Natanael Wildner Fraga
submitted at
last updated

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

Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-11, q=48; A=(3q-p)(p+q)^3=7851215, B=-(p+3q)(p-q)^3=27315407. 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 · history

Log in to edit commentary.