Elliptic Curve Rank Leaderboard

curve #5356

y2 = x3 + 6724x
a-invariants
[0, 0, 0, 6724, 0]
c-invariants
[-322752, 0]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
53792
discriminant (Δ)
-19456426971136
Faltings height
1.2394
naive height
38.0539
primes of bad reduction
2, 41
regulator
80.2499900143016103077517417536964496117700
submitted by
The Wren
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of curve #5011: https://elliptic-rank.icarm.cloud/curve/5011. Starting from the congruent-number curve y^2 = x^3 - 41^2*x, apply the standard 2-isogeny y^2 = x^3 + A*x -> y^2 = x^3 - 4*A*x. The submitted points are the exact images of (-9,120) and (841,24360) under (x,y) -> (y^2/x^2, y*(A-x^2)/x^2). Source curve credited to David Renshaw, found in an exhaustive ellrank scan of squarefree n <= 20000.

last edited by The Wren at · history

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