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On fields of definition of torsion points of elliptic curves with complex multiplication

Luis V. Dieulefait , Enrique González-Jiménez and Jorge Jiménez Urroz


Data: "On the division polynomials for small or bad reduction primes"

Isomorphic classes of elliptic curves defined over Q with CM.

-D
f
Short Weierstrass model of ED,f
-3
1
     y2=x3 + 16
-3
2
     y2=x3-15 x+22
-3
3
     y2=x3 - 480 x + 4048
-4
1
     y2=x3+x
-4
2
     y2=x3 - 11 x + 14
-7
1
     y2=x3 - 2835x - 71442
-7
2
     y2=x3-595x+5586
-8
1
     y2=x3 - 4320 x + 96768
-11
1
     y2=x3 - 9504 x + 365904
-19
1
     y2=x3 - 608 x + 5776
-43
1
     y2=x3 - 13760 x + 621264
-67
1
     y2=x3 - 117920 x + 15585808
-163
1
     y2=x3 - 34790720 x + 78984748304

 

-D
f
Factorization of the p-division polynomial of ED,f
-3
1
-3
2
-3
3
-4
1
-4
2
-7
1
-7
2
-8
1
-11
1
-19
1
-43
1
-67
1
-163
1

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Last modified: 9/9/2009