Elliptic Curve Rank Leaderboard

← home  ·  all curves  ·  JSON ↓

curve #2701

y2 + xy = x3 − 26539x + 516344
a-invariants
[1, 0, 0, -26539, 516344]
rank (lower bound)
≥ 2
torsion subgroup
ℤ/2ℤ × ℤ/4ℤ
conductor (N)
52923
discriminant (Δ)
1080120253623489
Faltings height
1.5765
naive height
42.1727
primes of bad reduction
3, 13, 23, 59
regulator
7.68168555371930424908414156171208264936520
submitted by
David Renshaw
submitted at
last updated

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

Commentary

Cremona 52923f2 = LMFDB 52923.a5: https://www.lmfdb.org/EllipticCurve/Q/52923/a/5 Mordell–Weil rank exactly 2 (Cremona's tables). Conductor 52923, minimal discriminant 1080120253623489, torsion ℤ/2ℤ × ℤ/4ℤ. The witnesses are the generators from Cremona's tables.

last edited by David Renshaw at · history

Log in to edit commentary.