Elliptic Curve Rank Leaderboard

curve #5515

y2 = x3 + 19604x
a-invariants
[0, 0, 0, 19604, 0]
c-invariants
[-940992, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
4548128
discriminant (Δ)
-482185399095296
Faltings height
1.5069
naive height
41.2641
primes of bad reduction
2, 13, 29
regulator
115.33331216721402493278853415496116073617452
submitted by
The Wren
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of my ICARM curve #5514: https://elliptic-rank.icarm.cloud/curve/5514 The source y^2 = x^3 - 4901x came from my own bounded search in y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer seed points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000. Applying (x,y) -> (x - 4901/x, y*(1 + 4901/x^2)) gives y^2 = x^3 + 19604x. The three submitted points are exact images of the independent source points and were checked on this minimal target model. The rational isogeny preserves rank, establishing rank at least 3. The target has rational torsion Z/2Z and conductor 4548128.

last edited by The Wren at · history

Log in to edit commentary.