Geodesic
Arithmetic Invariants for a Class of Elliptic Curves
Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 155-168 Cet article a éte moissonné depuis la source Math-Net.Ru

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We study the main arithmetic invariants of elliptic curves with complex multiplication. These curves are defined over the field of rational numbers and possess nondegenerate nonsupersingular reduction. 
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I. S. Rakhimov. Arithmetic Invariants for a Class of Elliptic Curves. Matematičeskie trudy, Tome 6 (2003) no. 1, pp. 155-168. http://geodesic.mathdoc.fr/item/MT_2003_6_1_a5/

[1] Bashmakov M. I., “Kogomologii abelevykh mnogoobrazii”, Uspekhi mat. nauk, 27:6 (168) (1972), 25–66 | MR | Zbl

[2] Bashmakov M. I., Kirillov A. N., “Filtratsiya Lyutts formalnykh grupp”, Izv. AN SSSR. Ser. mat., 39:6 (1975), 1227–1239 | MR | Zbl

[3] Berkovich V. G., “O delenii na izogeniyu tochek ellipticheskikh krivykh”, Mat. sb., 93 (135):3 (1974), 467–486 | MR | Zbl

[4] Borevich Z. I., Shafarevich I. R., Teoriya chisel, Nauka, M., 1985

[5] Kassesl Dzh., Frelikh A., Algebraicheskaya teoriya chisel, Mir, M., 1969

[6] Koblits N., $p$-Adicheskie chisla, $p$-adicheskii analiz i $\zeta$-funktsii, Mir, M., 1982

[7] Manii Yu. I., “Krugovye polya i modulyarnye krivye”, Uspekhi mat. nauk, 26:6 (1971), 7–71 | Zbl

[8] Rakhimov I. S., “O pole opredeleniya tochek $p$-go poryadka ellipticheskikh krivykh s kompleksnym umnozheniem”, Uzbekskii mat. zhurn., 5–6 (2000), 62–65 | Zbl

[9] Rakhimov I. S., “O lokalnom pole opredeleniya tochek $p$-to poryadka ellipticheskikh krivykh”, Uzbekskii mat. zhurn., 1 (2001), 41–44

[10] Serr Zh.-P., Kogomologii Galua, Mir, M., 1968

[11] Serr Zh.-P., Abelevy $l$-adicheskie predstavleniya i ellipticheskie krivye, Mir, M., 1973

[12] Serr Zh.-P., Teit Dzh., “Khoroshaya reduktsiya abelevykh mnogoobrazii”, Matematika, 15:5 (1971), 140–165 | Zbl

[13] Faddeev D. K., “O gruppe klassov divizorov na nekotorykh algebraicheskikh krivykh”, Dokl. AN SSSR, 136:2 (1961), 296–298 | MR | Zbl

[14] Faddeev D. K., “Ob invariantakh divizorov dlya krivykh $x^\kappa(1-x)=y^l$ v $l$-adicheskom krugovom pole”, Tr. Mat. in-ta im. V. A. Steklova, 64, 1961, 284–293 | MR | Zbl

[15] Shafarevich I. R., “Obschii zakon vzaimnosti”, Mat. sb., 26:1 (1950), 113–146 | MR | Zbl

[16] Gross V. N., Arithmetic on Elliptic Curves with Complex Multiplication, Lecture Notes in Math., 776, Springer-Verlag, Berlin; Heidelberg; New York, 1980 | MR | Zbl

[17] Serre J.-P., “Groupes de Lie $l$-adiques attaches aux courbes elliptiques”, Colloques Int. Centre Nat. Rech. Sci., 143 (1966), 239–256 | MR | Zbl

[18] Tate J., “Duality theorems in Galois cohomology over number fields”, Proc. Int. Congr. Math. Stockholm, 1963, 288–295 | MR | Zbl

[19] Tate J., Algorithm for Determining the Type of Singular Fiber in an Elliptic Pencil. Modular Functions of One Variable, Lecture Notes in Math., 476, Springer-Verlag, Berlin, 1973 | MR

[20] Tate J., “The arithmethic of elliptic curves”, Invent. Math., 23 (1974), 179–206 | DOI | MR | Zbl