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curve #858

y2 + y = x3 − x2 − 7820x − 263580
a-invariants
[0, -1, 1, -7820, -263580]
rank (lower bound)
≥ 0
torsion subgroup
trivial
conductor (N)
11 ★ record for rank ≥ 0
discriminant (Δ)
-11 ★ record for rank ≥ 0
Faltings height
0.4967
naive height
38.5071
primes of bad reduction
11
regulator
1
submitted by
David Renshaw
submitted at
last updated

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Commentary

LMFDB 11.a1 (Cremona 11a2): https://www.lmfdb.org/EllipticCurve/Q/11/a/1 Mordell–Weil rank exactly 0 per LMFDB. Conductor 11, minimal discriminant -11, torsion trivial. 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): #1 by conductor, #1 by |minimal discriminant|.

last edited by David Renshaw at · history

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