Torsion group G       |G|       Parameterizing variety
=========================   ====   ==============================
          Z/20Z              20                  P^2

          Z/21Z              21                  P^2

       Z/3Z x Z/9Z           27                  P^2

          Z/30Z              30                  P^2

          Z/35Z              35     positive rank elliptic curve

       Z/6Z x Z/6Z           36                  P^2

      Z/3Z x Z/12Z           36                  P^2

          Z/40Z              40    positive rank elliptic surface

          Z/45Z              45     positive rank elliptic curve

      Z/2Z x Z/24Z           48                  P^2

       Z/7Z x Z/7Z           49                  P^0

      Z/5Z x Z/10Z           50    positive rank elliptic surface

          Z/60Z              60     positive rank elliptic curve

          Z/63Z              63                  P^0

       Z/8Z x Z/8Z           64                  P^2

   Z/2Z x Z/4Z x Z/8Z        64                  P^2

      Z/6Z x Z/12Z           72    positive rank elliptic surface

   Z/2Z x Z/6Z x Z/6Z        72    positive rank elliptic surface

   Z/2Z x Z/2Z x Z/24Z       96     positive rank elliptic curve

Z/2Z x Z/2Z x Z/4Z x Z/8Z   128    positive rank elliptic surface

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  Families of curves over Q of genus 2 such that G is contained
            in the torsion subgroup of the Jacobian.

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