Parity over the biquadratic field
Let . Biquadratic-field parity conjecture. Every elliptic curve has even Mordell–Weil rank over :
The proposed statement follows from the parity conjecture because every place of splits into an even number of places in , giving global root number . Its unconditional truth is open with the parity conjecture.
References
Primary source
Tim Dokchitser, “Notes on the Parity Conjecture”, arXiv:1009.5389 (2012).
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