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use surjection of J1(N) onto J0(N) for computing divisor of order #26

Closed kevinywlui closed 8 years ago

kevinywlui commented 8 years ago

Two new things:

  1. Use the surjection of J1(N) onto J0(N) for computing divisor of torsion order.
  2. Created a is_J0 and is_J1 method.
williamstein commented 8 years ago

Sorry to be dumb, but in what sense does this patch "use surjection of J1(N) onto J0(N) for computing divisor of order"??

kevinywlui commented 8 years ago

Opps. I had to get rid of the case where J1(N) had a free part. Now if J1(N)(Q)_tor is finite then we can return a divisor of #J0(N)(Q)_tor. This is in L355-358 of torsion_subgroup.py

williamstein commented 8 years ago

On Thursday, July 14, 2016, Kevin Lui notifications@github.com wrote:

Opps. I had to get rid of the case where J1(N) had a free part. Now if J1(N)(Q)_tor is finite then we can return a

J1(N) thins is always fi!nite!

I'm

divisor of #J0(N)(Q)_tor. This is in L355-358 of torsion_subgroup.py

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kevinywlui commented 8 years ago

Ack. Did not mean to write the first tor.

If J1(N) is finite then J0(N) is also finite so J1(N)=J1(N)_tor and J0(N)=J0(N)_tor. So we have a surjection of J1(N)_tor onto J0(N)_tor. So now a divisor of #J0(N)_tor is also a divisor of #J1(N)_tor.

williamstein commented 8 years ago

On Friday, July 15, 2016, Kevin Lui notifications@github.com wrote:

Ack. Did not mean to write the first tor.

If J1(N) is finite then J0(N) is also finite so J1(N)=J1(N)_tor and J0(N)=J0(N)_tor.

So we have a surjection of J1(N)_tor onto J0(N)_tor.

Why?? A surjection of abvars does not imply surjection on rational points...

So now a divisor of #J0(N)_tor is also a divisor of #J1(N)_tor.

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kevinywlui commented 8 years ago

Oh right. My bad.