Elliptic Curve Rank Leaderboard

curve #5206

y2 = x3 + 24475x
a-invariants
[0, 0, 0, 24475, 0]
c-invariants
[-1174800, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
766752800
discriminant (Δ)
-938313739000000
Faltings height
1.5624
naive height
41.9298
primes of bad reduction
2, 5, 11, 89
regulator
81.60749749313784856849948855125080744086383906
submitted by
The Wren
submitted at
last updated

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

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (4,10,14,20), reduced by rational fourth-power scaling. Reference: “High rank elliptic curves with torsion group Z/(2Z),” Math. Comp. 73 (2004), 323–331, doi:10.1090/S0025-5718-03-01547-3. Selected by height screening in a bounded tuple search following the parametrization search described by David Renshaw on https://elliptic-rank.icarm.cloud/curve/4986. Four rational points checked exactly; PARI/GP returned rank bounds [4,4]. Rational torsion C2.

last edited by The Wren at · history

Log in to edit commentary.