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Does there exist infinitely many quadratic field such that rank of elliptic curves gains at most 2?

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#number-theory #algebraic-geometry #elliptic-curves #arithmetic-geometry
35
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Let $E/\Bbb{Q}$ be an elliptic curve. Let $K=\Bbb{Q}(\sqrt{D})$ be an quadratic number field.

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#number-theory #algebraic-number-theory #elliptic-curves #arithmetic-geometry
52
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Basepoint free line bundle on Blow up

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#algebraic-geometry #arithmetic-geometry #intersection-theory
129
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Maximal p-extension and pro-p extension

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#algebraic-number-theory #arithmetic #noncommutative-algebra #arithmetic-geometry #class-field-theory
54
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Twist of 2-Selmer group can be arbitrary large

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#number-theory #algebraic-geometry #elliptic-curves #arithmetic-geometry
351
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Does there exist a midsquare with natural sides and diagonal?

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#geometry #number-theory #elementary-number-theory #modular-arithmetic #arithmetic-geometry
51
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Conductor of determinant of a Galois representation divides the conductor of the representation

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#number-theory #algebraic-number-theory #characters #arithmetic-geometry #galois-representations
55
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Isomorphism between $2y^2=x^4-17$ and $y^2=x^3+17x$ over quadratic field

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#abstract-algebra #number-theory #elliptic-curves #arithmetic-geometry
111
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Which is isomorphic to $2y^2=x^4-17$ ?, $y^2=-34x^4+2$ or $y^2=-34x^4-2$

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#abstract-algebra #number-theory #algebraic-geometry #elliptic-curves #arithmetic-geometry
125
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coordinate of abelian variety and formal group

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#arithmetic-geometry #abelian-varieties
103
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Twist of Elliptic curve $E_D: Dy^2=x^3+ax+b$ is not isomorphic to $E:y^2=x^3+ax+b$?

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#algebraic-geometry #algebraic-number-theory #elliptic-curves #arithmetic-geometry
78
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On the definition of tilting of a perfectoid field

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#number-theory #commutative-algebra #algebraic-number-theory #arithmetic-geometry #galois-representations
34
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Almost purity for perfectoid fields applied on a computation of Galois cohomology.

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#number-theory #arithmetic-geometry #galois-representations #galois-cohomology
43
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Does there exist an elliptic curve $E/\Bbb{Q}$ such that for all quadratic number field $K$, $rank(E/K)=0$?

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#number-theory #algebraic-number-theory #elliptic-curves #algebraic-curves #arithmetic-geometry
54
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Why is the rank of elliptic curves isogeny invariant?

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#number-theory #elliptic-curves #arithmetic-geometry #isogeny

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