Complex Multiplication Tests for Elliptic Curves
نویسنده
چکیده
We consider the problem of checking whether an elliptic curve defined over a given number field has complex multiplication. We study two polynomial time algorithms for this problem, one randomized and the other deterministic. The randomized algorithm can be adapted to yield the discriminant of the endomorphism ring of the curve.
منابع مشابه
Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer
1. Quick Review of Elliptic Curves 2 2. Elliptic Curves over C 4 3. Elliptic Curves over Local Fields 6 4. Elliptic Curves over Number Fields 12 5. Elliptic Curves with Complex Multiplication 15 6. Descent 22 7. Elliptic Units 27 8. Euler Systems 37 9. Bounding Ideal Class Groups 43 10. The Theorem of Coates and Wiles 47 11. Iwasawa Theory and the “Main Conjecture” 50 12. Computing the Selmer G...
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