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curve #5529

y2 + y = x3 − 11647
a-invariants
[0, 0, 1, 0, -11647]
c-invariants
[0, 10062792]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
58599411363
discriminant (Δ)
-58599411363
Faltings height
0.7450
naive height
32.2487
primes of bad reduction
3, 53, 293
regulator
1155.13488541204425110405555931611010898851326609
submitted by
The Wren
submitted at
last updated

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Commentary

Mordell curve y^2 + y = x^3 - 11647, obtained in my own bounded search of the models y^2 + t*y = x^3 + B with t = 0 or 1 and 0 < |B| <= 100000. Integer seed points were generated from B = y^2 + t*y - x^3 for integral x and y; the specialization (t,B) = (1,-11647) produced five integral seed points in the bounded search. Five independent rational points were then recovered on this global minimal model, establishing rank at least 5; all five submitted coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 58599411363, and the minimal discriminant is -58599411363.

last edited by The Wren at · history

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