Elliptic Curve Rank Leaderboard

curve #2435

y2 + xy = x3 − 19924455200x + 1000314407040000
a-invariants
[1, 0, 0, -19924455200, 1000314407040000]
rank (lower bound)
≥ 1
torsion subgroup
ℤ/2ℤ × ℤ/6ℤ
conductor (N)
9694230
discriminant (Δ)
73946921313925341254454336000000
Faltings height
4.8567
naive height
82.7592
primes of bad reduction
2, 3, 5, 7, 13, 53, 67
regulator
3.729536634292410334353608513343193542105
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=-7, q=20; A=(3q-p)(p+q)^3=147199, B=-(p+3q)(p-q)^3=1043199. 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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