Elliptic Curve Rank Leaderboard

curve #2430

y2 + xy = x3 − 24597360150x − 1426312718977500
a-invariants
[1, 0, 0, -24597360150, -1426312718977500]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
567210
discriminant (Δ)
73612772815360236129000000000000
Faltings height
4.8772
naive height
83.3913
primes of bad reduction
2, 3, 5, 7, 37, 73
regulator
5.706682793305213160948199634809569339676
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=-37, q=12; A=(3q-p)(p+q)^3=-1140625, B=-(p+3q)(p-q)^3=-117649. 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.