Elliptic Curve Rank Leaderboard

curve #2478

y2 + xy + y = x3 − x2 − 1972829462x + 28273934936549
a-invariants
[1, -1, 1, -1972829462, 28273934936549]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
3652110
discriminant (Δ)
146079823177194035059161000000
Faltings height
4.3165
naive height
75.8218
primes of bad reduction
2, 3, 5, 7, 11, 17, 31
regulator
5.538606017431691919934157852058505756997
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=-21, q=10; A=(3q-p)(p+q)^3=-67881, B=-(p+3q)(p-q)^3=268119. 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.