Elliptic Curve Rank Leaderboard

curve #3388

y2 + xy = x3 − 29540772984030x + 74373317733156264900
a-invariants
[1, 0, 0, -29540772984030, 74373317733156264900]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/9ℤ
conductor (N)
8327367510
discriminant (Δ)
-739706710209979539570592866413751000000000
Faltings height
6.7510
naive height
105.0344
primes of bad reduction
2, 3, 5, 7, 11, 331, 10891
regulator
21.2087435722351243116767456669401933184984
submitted by
David Renshaw
submitted at
last updated

Witness: 2 independent points log in to add more points →

Commentary

Found in a rational-parameter search of the Kubert–Tate family for torsion ℤ/9ℤ: y^2 + (1-c)xy - by = x^3 - bx^2 with c=t^2(t-1), b=c(t^2-t+1), at t = -11/10; converted to the global minimal model. The 2 witness points were found with PARI/GP ellrank. Conductor 8327367510, torsion ℤ/9ℤ.

last edited by David Renshaw at · history

Log in to edit commentary.