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curve #859

y2 + y = x3 − x2 − 10x − 20
a-invariants
[0, -1, 1, -10, -20]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/5ℤ
conductor (N)
11 ★ record for rank ≥ 0
discriminant (Δ)
-161051
Faltings height
-0.3080
naive height
19.8078
primes of bad reduction
11
regulator
1
submitted by
David Renshaw
submitted at
last updated

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Commentary

LMFDB 11.a2 (Cremona 11a1): https://www.lmfdb.org/EllipticCurve/Q/11/a/2 Mordell–Weil rank exactly 0 per LMFDB. Conductor 11, minimal discriminant -161051, torsion ℤ/5ℤ. Submitted as one of the ten smallest rank-0 curves in LMFDB (as of 2026-09-23; places in LMFDB sort order, ties broken by label): #2 by conductor.

last edited by David Renshaw at · history

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