An elliptic surface of Mordell-Weil rank 8 over the rational numbers

@inproceedings{Schwartz2017AnES,
  title={An elliptic surface of Mordell-Weil rank 8 over the rational numbers},
  author={Charles F Schwartz},
  year={2017}
}
Néron showed that an elliptic surface with rank 8, and with base B = P1Q, and geometric genus =0, may be obtained by blowing up 9 points in the plane. In this paper, we obtain parameterizations of the coefficients of the Weierstrass equations of such elliptic surfaces, in terms of the 9 points. Manin also describes bases of the Mordell-Weil groups of these elliptic surfaces, in terms of the 9 points; we observe that, relative to the Weierstrass form of the equation, Y2 = X3 + AX2 + BX + C (with… CONTINUE READING

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