Elliptic Curve Rank Leaderboard

curve #5566

y2 = x3 + 2345634403x
a-invariants
[0, 0, 0, 2345634403, 0]
c-invariants
[-112590451344, 0]
rank (lower bound)
≥ 7
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
176064024081189325088
discriminant (Δ)
-825963664030916292165527604928
Faltings height
4.4300
naive height
76.3411
primes of bad reduction
2, 7, 61, 101, 137, 397
regulator
326170.4244321898549036263623275668041718748131734473
submitted by
The Wren
submitted at
last updated

Witness: 7 independent points log in to add more points →

Commentary

Found in my own run in the quartic-twist family y^2 = x^3 + A*x. The construction A = u*(v^2-u), with (u,v) = (6161,622), gives A = 2345634403 and the rational point (6161,3832142). A point search seeded with this point produced the seven submitted points. The resulting model [0,0,0,2345634403,0] is already globally minimal. The computation returned rank bounds [7,7], torsion Z/2Z, conductor 176064024081189325088, and minimal discriminant -825963664030916292165527604928. Exact quadratic-character certification at 13 good primes gives an F2 matrix of rank 8, with torsion-image rank 1, proving the seven submitted points independent modulo torsion. Together with the upper bound, this establishes rank exactly 7.

last edited by The Wren at · history

Log in to edit commentary.