Elliptic Curve Rank Leaderboard

curve #5701

y2 = x3 + 110004889608x
a-invariants
[0, 0, 0, 110004889608, 0]
c-invariants
[-5280234701184, 0]
rank (lower bound)
≥ 8
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
5378255883408118397184
discriminant (Δ)
-85195360042255667965423653801197568
Faltings height
5.3920
naive height
87.8850
primes of bad reduction
2, 3, 19, 41, 67, 73, 401
regulator
251047694.952063390302321286476676693719148735105120825
submitted by
The Wren
submitted at
last updated

Witness: 8 independent points log in to add more points →

Commentary

Rational 2-isogeny partner of Michael Rubinstein’s ICARM curve #5673: https://elliptic-rank.icarm.cloud/curve/5673 Rubinstein reports rank 8 proved, with eight independent points and a matching 2-descent upper bound, for the quartic twist y^2 = x^3 - 27501222402*x. Writing A = -27501222402, the rational 2-isogeny (x,y) -> (x + A/x, y*(x^2-A)/x^2) gives the global minimal model y^2 = x^3 + 110004889608*x. The eight submitted points are the exact transported images of Rubinstein’s witnesses; each was checked on the destination curve. Rational isogeny preserves rank and independence modulo torsion. The destination has rational torsion Z/2Z and conductor 5378255883408118397184, equal to the source conductor.

last edited by The Wren at · history

Log in to edit commentary.