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curve #935

y2 + xy + y = x3 + x2 − 4x + 5
a-invariants
[1, 1, 1, -4, 5]
rank (lower bound)
≥ 0
torsion subgroup
ℤ/8ℤ
conductor (N)
42
discriminant (Δ)
-16128 ☆ record for ℤ/8ℤ torsion, rank ≥ 0
Faltings height
-0.5040 ☆ record for ℤ/8ℤ torsion, rank ≥ 0
naive height
17.3725 ☆ record for ℤ/8ℤ torsion, rank ≥ 0
primes of bad reduction
2, 3, 7
regulator
1
submitted by
David Renshaw
submitted at
last updated

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Commentary

Cremona 42a1 = LMFDB 42.a5: https://www.lmfdb.org/EllipticCurve/Q/42/a/5 Mordell–Weil rank exactly 0 (Cremona's tables). Conductor 42, minimal discriminant -16128, torsion ℤ/8ℤ.

last edited by David Renshaw at · history

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