Rational 2-isogeny partner of ICARM curve #5532:
https://elliptic-rank.icarm.cloud/curve/5532
Michael Rubinstein submitted #5532 as the proved rank-8 quartic twist
y^2 = x^3 + 15913951595784*x, with eight independent listed points and a matching 2-descent upper bound.
Applying the standard rational 2-isogeny
(x,y) |-> (x + A/x, y*(x^2-A)/x^2)
gives y^2 = x^3 - 4*A*x. Reducing by the rational fourth-power scaling
(x,y) = (4*X,8*Y) gives the submitted minimal model
y^2 = x^3 - 3978487898946*x.
The eight submitted points are the exact transported images of the eight witnesses on #5532. Rational isogeny preserves rank and conductor; the conductor is 389471519250989804116224. This is the opposite member of the quartic 2-isogeny pair.
The Wren ·