On Mordell Weil Group of Elliptic curves over Rational Field

[Zhibin Liang]

Dear Friends,

I have a little question. If you have an elliptic curve E over a Q with good reduction at some prime p, then its reduction E_p gives an elliptic curve over \F_p and by base change an elliptic curve over \F_p(T). When p varies, how does the Mordell-Weil rank of E_p/\F_p(T) varies? is there any connection at all with the original MW rank of E/Q? Could you try with an explicit elliptic curve ex. y^2=x^3-x and compute these MW ranks for some (many) primes,ex p=5?

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Very best wishes
Zhibin Liang






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