P. Cohen, On the coecients of the transformation polynomials for the elliptic modular function, Math. Proc. Cambridge Philos. Soc. 95 (1984), 389-402. Home/Search Document Not in Database Summary Related Articles Check |
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A Measure Of Simultaneous Approximation For Quasi-Modular Functions - Grinspan (Correct)
....over Q( and e 1 the highest power of dividing N ; then the quotients = N = e 1 and = N = e 1 belong to Q( X ] and the identity ( 0 ( yields the expected result. 3. The ideas here are mainly those of [Coh84]. De ne, as we did above for N and N , the specializations N (X) N (X; 16 ) X N (X) XN (X; 16 ) We then have the Lemma 4. cf. Coh84] x5) log L( N ) log sup 2[1;2] L( i N ) O( N) log L(XN ) log sup 2[1;2] L(X i N ) O( N) Thus all we have ....
....] and the identity ( 0 ( yields the expected result. 3. The ideas here are mainly those of [Coh84] De ne, as we did above for N and N , the specializations N (X) N (X; 16 ) X N (X) XN (X; 16 ) We then have the Lemma 4. cf. [Coh84], x5) log L( N ) log sup 2[1;2] L( i N ) O( N) log L(XN ) log sup 2[1;2] L(X i N ) O( N) Thus all we have to do is bound, uniformly in 2 [1; 2] the height of polynomials i N , X i N in one variable. Then, the same reasoning as in [Coh84] Lemma 1, reduces it to ....
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P. Cohen. On the coecients of the transformation polynomials for the elliptic modular function. Math. Proc. Camb. Phil. Soc., 95(3):389-402, 1984.
Isogeny volcanoes and the SEA algorithm - Fouquet, Morain (2000) (Correct)
.... 3 1855425871872000000000Y 770845966336000000XY 8900222976000X 2 Y 1069956X 3 Y 452984832000000Y 2 8900222976000XY 2 2587918086X 2 Y 2 2232X 3 Y 2 36864000Y 3 1069956XY 3 2232X 2 Y 3 X 3 Y 3 : More generally, the coecients of tend to explode [2]. In the most optimized versions of Elkies s algorithm, special modular equations are used, that have smaller coecients. We are not concerned by this aspect here and refer the reader to [19, 21] for more details. Note that in real life, it is easy to use these alternative equations to perform the ....
.... one of the curves isogenous to G[i] and S[i] contains a list of curves isogenous to G 0 [i] IF S[i] THEN use next i; IF #S[i] 1 THEN fi 0 i; we have found the oor)g ELSE (a) IF (j(S[i] 1] j(G[i] THEN f(we must not come back to the preceding curve) G[i] G 0 [i] G 0 [i] S[i][2];g; ELSE fG[i] G 0 [i] G 0 [i] S[i] 1] g; b) P [i] P [i] fG 0 [i]g; c) IF G 0 [i] is special THEN S[i] ELSE S[i] IsogenousCurves(G 0 [i] 6. RETURN P [i 0 ] Lemma 2.5 ensures us that whenever we have an isogeny : E E 0 such that is #, every isogeny : E 0 ....
P. Cohen. On the coecients of the transformation polynomials for the elliptic modular function. Math. Proc. Cambridge Philos. Soc., 95:389-402, 1984.
Remarks on Codes From Modular Curves: - Maple Applications David (Correct)
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P. Cohen, On the coecients of the transformation polynomials for the elliptic modular function, Math. Proc. Cambridge Philos. Soc. 95 (1984), 389-402.
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