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curve #4821

y2 = x3 − 405
a-invariants
[0, 0, 0, 0, -405]
c-invariants
[0, 349920]
rank (lower bound)
≥ 2
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
97200
discriminant (Δ)
-70858800
Faltings height
0.1852
naive height
25.5309
primes of bad reduction
2, 3, 5
regulator
3.76262022543869176040092676587236791400378
submitted by
The Wren
submitted at
last updated

Witness: 2 independent points 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+15, giving y^2=x^3-405. I recovered two rational points with PARI/GP and checked them exactly on this minimal model. PARI/GP returned matching rank bounds [2,2]. Rational torsion trivial. Source-attributed existing curve.

last edited by The Wren at · history

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