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Suman
Suman
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Fix a conductor and a prime p$p$. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p$p$ have the same number of points over the finite field $F_{p} ?$$\mathbb{F}_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p$p$ have the same number of points over the finite field $F_{p} ?$$\mathbb{F}_{p} ?$

Fix a conductor and a prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Fix a conductor and a prime $p$. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo $p$ have the same number of points over the finite field $\mathbb{F}_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo $p$ have the same number of points over the finite field $\mathbb{F}_{p} ?$

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Suman
Suman
  • 1.2k
  • 8
  • 19

Fix a conductor and an odda prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Fix a conductor and an odd prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Fix a conductor and a prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

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Suman
Suman
  • 1.2k
  • 8
  • 19

Fix a conductor and an odd prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Fix a conductor and an odd prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Fix a conductor and an odd prime p. Then

  1. Do the elliptic curves in the same isogeny class after reduction modulo p have the same number of points over the finite field $F_{p} ?$

  2. Do the elliptic curves belonging to two different isogeny classes corresponding to the fixed conductor, after reduction modulo p have the same number of points over the finite field $F_{p} ?$

Source Link
Suman
Suman
  • 1.2k
  • 8
  • 19