Equations for Modular Curves - Magma

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Notation Modularity Finiteness Results Computationality g = 0,1 g = 2 g ≥ 2 Let g ∈ Z such that g ≥ 0, we denote by M C g = {modular curves of genus g} / Q , M C new g = {[C] ∈ M C g |C is new}. Enrique González Jiménez Equations for Modular Curves
Notation Modularity Finiteness Results Computationality g = 0,1 g = 2 g ≥ 2 Let g ∈ Z such that g ≥ 0, we denote by M C g = {modular curves of genus g} / Q , M C new g = {[C] ∈ M C g |C is new}. 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 45 and 46: Fact Modularity Finiteness Results
Page 47: Fact Modularity Finiteness Results
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
Page 89 and 90: Notation Modularity Finiteness Resu
Page 95 and 96: Conjecture 1 Modularity Finiteness
Page 97 and 98: Hyperelliptic Curves Definition Mod
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Hyperelliptic Curves Definition Mod
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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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