Elliptic Curve Rank Leaderboard

curve #2509

y2 + xy = x3 − 122113825x + 517966255625
a-invariants
[1, 0, 0, -122113825, 517966255625]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
2451570
discriminant (Δ)
634436293376798649000000
Faltings height
3.4343
naive height
67.4750
primes of bad reduction
2, 3, 5, 11, 17, 19, 23
regulator
2.780307562480580404796662585662437171038
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=-17, q=2; A=(3q-p)(p+q)^3=-77625, B=-(p+3q)(p-q)^3=-75449. 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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