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curve #5525

y2 + y = x3 − 12746
a-invariants
[0, 0, 1, 0, -12746]
c-invariants
[0, 11012328]
rank (lower bound)
≥ 5
torsion subgroup
trivial
family
y2 = x3 + k (Mordell curves)
conductor (N)
70180189803
discriminant (Δ)
-70180189803
Faltings height
0.7601
naive height
32.4291
primes of bad reduction
3, 17, 2999
regulator
1112.67192654514494091511464864359093397524712997
submitted by
The Wren
submitted at
last updated

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Commentary

Mordell curve y^2 + y = x^3 - 12746, 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 using B = y^2 + t*y - x^3 for integer x from -47 to 10000. The specialization (t,B) = (1,-12746) supplied seven integral seed points. Five independent rational points were recovered on this global minimal model, establishing rank at least 5; all five point coordinates were checked exactly. The rational torsion subgroup is trivial, the conductor is 70180189803, and the minimal discriminant is -70180189803.

last edited by The Wren at · history

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