Elliptic Curve Rank Leaderboard

curve #2527

y2 + xy = x3 − 34455551x + 60270994905
a-invariants
[1, 0, 0, -34455551, 60270994905]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
1607970
discriminant (Δ)
1048497620162995169294400
Faltings height
3.3212
naive height
63.6791
primes of bad reduction
2, 3, 5, 7, 13, 19, 31
regulator
3.795196800582035512261648364052845410000
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=-13, q=6; A=(3q-p)(p+q)^3=-10633, B=-(p+3q)(p-q)^3=34295. 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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