Elliptic Curve Rank Leaderboard

curve #5094

y2 = x3 + 176358x
a-invariants
[0, 0, 0, 176358, 0]
c-invariants
[-8465184, 0]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/2ℤ
family
y2 = x3 + ax (quartic twists)
conductor (N)
1990537226496
discriminant (Δ)
-351047164190381568
Faltings height
2.0561
naive height
47.8544
primes of bad reduction
2, 3, 7, 13, 17, 19
regulator
218.1755669272051790496590610311079079337337216
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 (5,7,11,15), 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.