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curve #861

y2 + xy + y = x3 − 171x − 874
a-invariants
[1, 0, 1, -171, -874]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/2ℤ
conductor (N)
14 ☆ record for ℤ/2ℤ torsion, rank ≥ 0
discriminant (Δ)
-1835008
Faltings height
0.0665
naive height
27.0359
primes of bad reduction
2, 7
regulator
1
submitted by
David Renshaw
submitted at
last updated

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Commentary

LMFDB 14.a2 (Cremona 14a3): https://www.lmfdb.org/EllipticCurve/Q/14/a/2 Mordell–Weil rank exactly 0 per LMFDB. Conductor 14, minimal discriminant -1835008, torsion ℤ/2ℤ. 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): #5 by conductor.

last edited by David Renshaw at · history

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