Integral Points of Elliptic Curve y^2 = x^3+3x

Theorem

The elliptic curve:

$y^2 = x^3 + 3 x$

has exactly $7$ lattice points:

$\tuple {0, 0}, \tuple {1, \pm 2}, \tuple {3, \pm 6}, \tuple {12, \pm 42}$

Proof

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Sources

• The LMFDB Collaboration, The L-functions and Modular Forms Database, Elliptic Curve 288/a/2, $2013$ [Online; accessed 18-Jul-2019]