Elliptic Curve Rank Leaderboard

curve #3689

y2 + xy = x3 − 978101465x + 172191466601817
a-invariants
[1, 0, 0, -978101465, 172191466601817]
rank (lower bound)
≥ 4
torsion subgroup
ℤ/5ℤ
conductor (N)
4317455370
discriminant (Δ)
-12748882549946802125976562500000
Faltings height
4.6480
naive height
79.0824
primes of bad reduction
2, 3, 5, 139, 1035361
regulator
393.6762163569255855409194524812951873433580458
submitted by
Michael Rubinstein
submitted at
last updated

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Commentary

Specialization at t = -417/250 of the universal curve with a 5-torsion point, y^2 + (t+1)xy + ty = x^3 + tx^2 (as searched in arXiv:2003.00077, Sec. 12), found by searching small-height t = a/b for small conductor, with points from a 2-descent (PARI ellrank).

last edited by Michael Rubinstein at · history

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