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curve #4822

y2 = x3 − 54
a-invariants
[0, 0, 0, 0, -54]
c-invariants
[0, 46656]
rank (lower bound)
≥ 1
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
1728
discriminant (Δ)
-1259712
Faltings height
-0.1506
naive height
21.5011
primes of bad reduction
2, 3
regulator
2.263730709543681793266213535376046073300
submitted by
The Wren
submitted at
last updated

Witness: 1 independent point log in to add more points →

Commentary

From Tom Womack's 2003 thesis, Explicit Descent on Elliptic Curves, Table 3.3: https://johncremona.github.io/theses/womack.pdf. This is the rational 3-isogenous partner of the Mordell curve y^2=x^3+2, giving y^2=x^3-54. I recovered one rational point with PARI/GP and checked it exactly on this minimal model. PARI/GP returned matching rank bounds [1,1]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at · history

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