Equations for Modular Curves - Magma

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Theorem Modularity Finiteness Results Computationality Let C /Q be an elliptic curve. Then ∃π /Q : X0(N) for some positive integer N. Departure point Generalization Newness C , A. Wiles, Modular elliptic curves and Fermat’s Last Theorem, Ann. Math. 141 (1995), 443–551. C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14(4) (2001), 843–939. Enrique González Jiménez Equations for Modular Curves
Theorem Modularity Finiteness Results Computationality Let C /Q be an elliptic curve. Then ∃π /Q : X0(N) for some positive integer N. Departure point Generalization Newness C , A. Wiles, Modular elliptic curves and Fermat’s Last Theorem, Ann. Math. 141 (1995), 443–551. C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14(4) (2001), 843–939. Enrique González Jiménez Equations for Modular Curves
Page 1 and 2: Modularity Finiteness Results Compu
Page 5: Theorem Modularity Finiteness Resul
Page 9 and 10: Generalization Modularity Finitenes
Page 17 and 18: Definition Modularity Finiteness Re
Page 45 and 46: Fact Modularity Finiteness Results
Page 47 and 48: Fact Modularity Finiteness Results
Page 49 and 50: Notation Modularity Finiteness Resu
Page 51 and 52: g = 0 M C 0 = M C new 0 #M C 0 = #M
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g = 0 M C 0 = M C new 0 #M C 0 = #M
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g = 0 M C 0 = M C new 0 #M C 0 = #M
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g = 2 Theorem #M C new 2 < ∞ Modu
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Theorem #M C new 2 < ∞ Moreover,
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Theorem #M C new 2 < ∞ Moreover,
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Theorem #M C new 2 = 213 Moreover,
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C : y 2 = F(x) Modularity Finitenes
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g ≥ 2 Theorem Modularity Finitene
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Notation Modularity Finiteness Resu
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Conjecture 1 Modularity Finiteness
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Hyperelliptic Curves Definition Mod
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Algorithm Modularity Finiteness Res
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Algorithm (cont.) Modularity Finite
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Modularity Finiteness Results Compu
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C A 21A {0,2} C : y 2 = F(x) Modula
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C A 21A {0,2} C : y 2 = F(x) Modula
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C A 21A {0,2} C : y 2 = F(x) Modula
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C A 21A {0,2} C : y 2 = F(x) Modula
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C A 21A {0,2} C : y 2 = F(x) Modula
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Conjecture #M C new (2) = 300 Modul
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Example Modularity Finiteness Resul
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C X1(17) : ⎧ ⎨ ⎩ Modularity F
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Final Remark k a field, char(k) = 0
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