Elliptic Curve Rank Leaderboard

curve #2475

y2 + xy = x3 − 2277024176x + 40976555854080
a-invariants
[1, 0, 0, -2277024176, 40976555854080]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
2929290
discriminant (Δ)
30215784460288861700098560000
Faltings height
4.2509
naive height
76.2520
primes of bad reduction
2, 3, 5, 7, 13, 29, 37
regulator
4.517886462418831008994975825862085405010
submitted by
Natanael Wildner Fraga
submitted at
last updated

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Commentary

Exact computational search in the full 2-torsion/3-torsion family with p=-25, q=4; A=(3q-p)(p+q)^3=-342657, B=-(p+3q)(p-q)^3=-317057. 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

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