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curve #871

y2 + xy + y = x3
a-invariants
[1, 0, 1, 0, 0]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/3ℤ
conductor (N)
26
discriminant (Δ)
-26
Faltings height
-1.0442
naive height
10.3970 ☆ record for ℤ/3ℤ torsion, rank ≥ 0
primes of bad reduction
2, 13
regulator
1
submitted by
David Renshaw
submitted at
last updated

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Commentary

LMFDB 26.a3 (Cremona 26a3): https://www.lmfdb.org/EllipticCurve/Q/26/a/3 Mordell–Weil rank exactly 0 per LMFDB. Conductor 26, minimal discriminant -26, torsion ℤ/3ℤ. 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): #6 by Faltings height, #9 by |minimal discriminant|.

last edited by David Renshaw at · history

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