List questions from arithmetic-geometry

Published on 28 Jun 2023 - 21:08

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degree 2 isogeny $\phi : E\to E'$ given by $(x,y)\to (\frac{y^2}{x^2},\frac{y(a-x^2)}{x^2})$ and $\phi(0,0)$

Published on 05 Jul 2023 - 8:53

108

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What is the definition of $Sha(E/K)[\phi]$ for elliptic curves?

Published on 05 Jul 2023 - 11:24

51

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Finite subgroups of $\text{PGL}_N(\mathbf{Z})$

Published on 06 Jul 2023 - 13:18

130

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Let $E:y^2=x^3+17x$. Let $K=\Bbb{Q}(\sqrt{D})$($D$ is a negative integer). If $D\neq -17$, I want to prove $E(K)_{tor}\cong \Bbb{Z}/2\Bbb{Z}$.

Published on 10 Jul 2023 - 19:03

77

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Contradiction caused by 2-isogeny of elliptic curves?

Published on 11 Jul 2023 - 7:35

110

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Why is $\text{End}(E)\cong\mathbb{Z}[i]$

Published on 11 Jul 2023 - 15:39

137

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Morphisms that are injective and surjective but not isomorphisms

Published on 23 Feb 2026 - 12:02

36

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Sieves in arithmetic geometry

Published on 25 Mar 2026 - 14:28

89

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Induced map on the 2-part of an abelian group

Published on 16 Jul 2023 - 18:19

33

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cardinality of a set in diophantine geometry

Published on 18 Jul 2023 - 11:07

77

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An exact sequence $1 \to {O_{K,S}}^{\times}/{{O_{K,S}}^{\times}}^2 \to K(S,2) \to Cl(K,S)[2] \to 1$

Published on 25 Mar 2026 - 4:43

116

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Definition of Hodge tensor

Published on 26 Mar 2026 - 14:33

81

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Neukirch 'Algebraic number theory', p73, Prop 11.6. there is a surjection $Cl(O) \to Cl(O(X))$.

Published on 25 Mar 2026 - 4:42

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Corollary 6.4:Arithmetic of Elliptic Curves,Silverman

Published on 23 Feb 2026 - 10:22

List Question

Silverman Elliptic Curves Exercise 1.8

degree 2 isogeny $\phi : E\to E'$ given by $(x,y)\to (\frac{y^2}{x^2},\frac{y(a-x^2)}{x^2})$ and $\phi(0,0)$

What is the definition of $Sha(E/K)[\phi]$ for elliptic curves?

Finite subgroups of $\text{PGL}_N(\mathbf{Z})$

Let $E:y^2=x^3+17x$. Let $K=\Bbb{Q}(\sqrt{D})$($D$ is a negative integer). If $D\neq -17$, I want to prove $E(K)_{tor}\cong \Bbb{Z}/2\Bbb{Z}$.

Contradiction caused by 2-isogeny of elliptic curves?

Why is $\text{End}(E)\cong\mathbb{Z}[i]$

Morphisms that are injective and surjective but not isomorphisms

Sieves in arithmetic geometry

Induced map on the 2-part of an abelian group

cardinality of a set in diophantine geometry

An exact sequence $1 \to {O_{K,S}}^{\times}/{{O_{K,S}}^{\times}}^2 \to K(S,2) \to Cl(K,S)[2] \to 1$

Definition of Hodge tensor

Neukirch 'Algebraic number theory', p73, Prop 11.6. there is a surjection $Cl(O) \to Cl(O(X))$.

Corollary 6.4:Arithmetic of Elliptic Curves,Silverman

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