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curve #4820

y2 = x3 + 297
a-invariants
[0, 0, 0, 0, 297]
c-invariants
[0, -256608]
rank (lower bound)
≥ 2
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
13068
discriminant (Δ)
-38106288
Faltings height
0.1335
naive height
24.9106
primes of bad reduction
2, 3, 11
regulator
0.404128771490454734203976327400265637271859
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^3-11, giving y^2=x^3+297. 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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