Elliptic Curve Rank Leaderboard

curve #5513

y2 = x3 − 7585x
a-invariants
[0, 0, 0, -7585, 0]
c-invariants
[364080, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1841031200
discriminant (Δ)
27928443304000
Faltings height
1.2695
naive height
38.4154
primes of bad reduction
2, 5, 37, 41
regulator
109.4762318504211284567854174464636490951828772
submitted by
The Wren
submitted at
last updated

Witness: 4 independent points log in to add more points →

Commentary

Quartic twist y^2 = x^3 - 7585x, obtained in my own bounded search in the family y^2 = x^3 + Ax with 0 < |A| <= 30000. Integer points were generated using A = (y^2 - x^3)/x for nonzero integer x between -173 and 5000, retaining integral A. This search produced A = -7585. Four independent rational points were recovered and checked exactly on this minimal model, establishing rank at least 4. The rational torsion subgroup is Z/2Z and the conductor is 1841031200.

last edited by The Wren at · history

Log in to edit commentary.