Question

Show that $\mathcal C : Y^2=X(X^2-pX+p^2)$ has rank $0$, where $p$ is a prime $\equiv$ 2 (mod 3) and 5 (mod 8)

score 138 · Answer 1 · 2026-03-29 13:23:50

138

Views

Show that $\mathcal C : Y^2=X(X^2-pX+p^2)$ has rank $0$, where $p$ is a prime $\equiv$ 2 (mod 3) and 5 (mod 8)

Published on 29 Mar 2026 - 13:23

score 68 · Answer 2 · 2026-04-10 06:37:20

68

Views

The integral change if we change the domain.

Published on 10 Apr 2026 - 6:37

score 352 · Answer 3 · 2026-03-26 22:53:42

352

Views

Finding torsion points of given order on elliptic curve

Published on 26 Mar 2026 - 22:53

score 105 · Answer 4 · 2026-04-09 22:57:09

105

Views

How to prove $H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ to the lattice $\Lambda$ ,$\gamma \mapsto \int_\gamma dz$ is well defined?

Published on 09 Apr 2026 - 22:57

score 69 · Answer 5 · 2026-03-28 00:28:47

69

Views

$H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ → $\Lambda$ via the map $f:\gamma \mapsto \int_\gamma dz$ is surjective?

Published on 28 Mar 2026 - 0:28

score 52 · Answer 6 · 2026-03-29 13:29:05

52

Views

$H^1(E(C), Z_\ell)$ is isomorphic to $T_\ell(E(C))$ and Lefschetz principle

Published on 29 Mar 2026 - 13:29

score 195 · Answer 7 · 2026-04-02 04:35:05

195

Views

Holomorphic differential of elliptic curve over $\mathbb C$

Published on 02 Apr 2026 - 4:35

score 159 · Answer 8 · 2021-06-15 06:31:38

159

Views

Why $H^1(E(C), Z/nZ)$ is isomorphic to $H^1(E(C), Z)\bigotimes Z/nZ$?

Published on 15 Jun 2021 - 6:31

score 84 · Answer 9 · 2026-04-04 20:37:29

84

Views

Two rational function with same divisor over Eliptic Curve

Published on 04 Apr 2026 - 20:37

score 74 · Answer 10 · 2021-06-15 20:38:28

74

Views

Can I choose $E/\mathbb{F}_q$ so that $\#E(\mathbb{F}_q) = a$ for any $a \in \{1,\dots,q^2 \}$?

Published on 15 Jun 2021 - 20:38

score 220 · Answer 11 · 2021-06-16 07:07:02

220

Views

Adding two points in an elliptic curve gives the infinity point

Published on 16 Jun 2021 - 7:07

score 75 · Answer 12 · 2021-06-17 10:40:28

75

Views

Lower bound on height rational point (Lemma 1, Ch 7 from Cassels' Lectures on Elliptic Curves)

Published on 17 Jun 2021 - 10:40

score 141 · Answer 13 · 2026-03-25 09:23:57

141

Views

Example of complex multiplication for elliptic curve

Published on 25 Mar 2026 - 9:23

score 311 · Answer 14 · 2026-03-25 09:27:10

311

Views

Reduction of CM Elliptic Curves

Published on 25 Mar 2026 - 9:27

score 173 · Answer 15 · 2026-03-26 09:17:52

173

Views

Torsion parts of elliptic curve

Published on 26 Mar 2026 - 9:17

List Question

Show that $\mathcal C : Y^2=X(X^2-pX+p^2)$ has rank $0$, where $p$ is a prime $\equiv$ 2 (mod 3) and 5 (mod 8)

The integral change if we change the domain.

Finding torsion points of given order on elliptic curve

How to prove $H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ to the lattice $\Lambda$ ,$\gamma \mapsto \int_\gamma dz$ is well defined?

$H_1(\mathbb{C}/\Lambda, \mathbb{Z})$ → $\Lambda$ via the map $f:\gamma \mapsto \int_\gamma dz$ is surjective?

$H^1(E(C), Z_\ell)$ is isomorphic to $T_\ell(E(C))$ and Lefschetz principle

Holomorphic differential of elliptic curve over $\mathbb C$

Why $H^1(E(C), Z/nZ)$ is isomorphic to $H^1(E(C), Z)\bigotimes Z/nZ$?

Two rational function with same divisor over Eliptic Curve

Can I choose $E/\mathbb{F}_q$ so that $\#E(\mathbb{F}_q) = a$ for any $a \in \{1,\dots,q^2 \}$?

Adding two points in an elliptic curve gives the infinity point

Lower bound on height rational point (Lemma 1, Ch 7 from Cassels' Lectures on Elliptic Curves)

Example of complex multiplication for elliptic curve

Reduction of CM Elliptic Curves

Torsion parts of elliptic curve

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