Elliptic Curve Rank Leaderboard

curve #2440

y2 + xy + y = x3 − x2 − 15147988322x + 47730269371169
a-invariants
[1, -1, 1, -15147988322, 47730269371169]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
3028410
discriminant (Δ)
221472359491587460955015625000000
Faltings height
4.8961
naive height
81.9370
primes of bad reduction
2, 3, 5, 7, 11, 19, 23
regulator
5.284242946731528485434377188027896529674
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=-3, q=22; A=(3q-p)(p+q)^3=473271, B=-(p+3q)(p-q)^3=984375. 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.