Submitted by 
S.E.Fischer 
Date 
02/24/2017 
Reference 
Not available

Comments


Tags 
Explicit curves 
User comments
Same Isogeny Class for both examples

S.E.Fischer
03/20/2018 21:03

Both examples represent the same isogeny class given by the Real Weil Polynomial (x+49)^5.
This can be seen, since they both allow Galois Descent to (x+1)^5 over GF(25), whereas the only other (not yet excluded) possibility (of an isogeny class) given by the Real Weil Polynomial (x+46)(x+49)(x+50)^3 doesn't show such a possibility.

A possibly different curve

Everett Howe
06/27/2017 20:12

Matthieu Rambaud provides equations for a Shimura curve with 871 points (found in his draft paper "Shimura curves and multiplication"):
3*x^3*y^3 + 2*x^3*y + 4*x^3 + 4*x^2 + 2*x*y^3 + 3*x*y + 3*x + 2 = 0,
3*y^3*z^3 + 2*y^3*z + 4*y^3 + 4*y^2 + 2*y*z^3 + 3*y*z + 3*y + 2 = 0


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