Equations for Modular Curves - Magma

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Modularity Finiteness Results Computationality Equations for Modular Curves 1 Modularity Departure point Generalization Newness 2 Finiteness Results g = 0,1 g = 2 g ≥ 2 3 Computationality Hyperelliptic Curves Non-Hyperelliptic Curves Final Remark g = 0,1 g = 2 g ≥ 2 Enrique González Jiménez Equations for Modular Curves
Fact Modularity Finiteness Results Computationality g = 0,1 g = 2 g ≥ 2 If C /Q is modular of level N, then C(Q) = /0, since π /Q and i∞ ∈ X1(N)(Q). Enrique González Jiménez Equations for Modular Curves
Page 1 and 2: Modularity Finiteness Results Compu
Page 5 and 6: Theorem Modularity Finiteness Resul
Page 7 and 8: Theorem Modularity Finiteness Resul
Page 9 and 10: Generalization Modularity Finitenes
Page 17 and 18: Definition Modularity Finiteness Re
Page 43: Modularity Finiteness Results Compu
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
Page 61 and 62: g = 2 Theorem #M C new 2 < ∞ Modu
Page 63 and 64: Theorem #M C new 2 < ∞ Moreover,
Page 65 and 66: Theorem #M C new 2 < ∞ Moreover,
Page 67 and 68: Theorem #M C new 2 = 213 Moreover,
Page 73 and 74: C : y 2 = F(x) Modularity Finitenes
Page 87 and 88: g ≥ 2 Theorem Modularity Finitene
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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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Equations for Modular Curves - Magma

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