Elliptic Curve Rank Leaderboard

curve #5195

y2 = x3 + 4488x
a-invariants
[0, 0, 0, 4488, 0]
c-invariants
[-215424, 0]
rank (lower bound)
≥ 3
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
80568576
discriminant (Δ)
-5785468305408
Faltings height
1.1383
naive height
36.8411
primes of bad reduction
2, 3, 11, 17
regulator
29.595254924420519147989644223541673498277410
submitted by
The Wren
submitted at
last updated

Witness: 3 independent points log in to add more points →

Commentary

Obtained from the Aguirre–Castaneda–Peral parametrization at tuple (3,6,15,18), 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. Three rational points checked exactly; PARI/GP returned rank bounds [3,3]. Rational torsion C2.

last edited by The Wren at · history

Log in to edit commentary.