From Andrej Dujella and Juan Carlos Peral’s prescribed-torsion rank table, z2z2old1011121314.html: https://dujella.github.io/tors/z2z2old1011121314.html
Twelve supplied rational points checked exactly on the displayed model; the source lists them as independent. Rational torsion Z/2Z × Z/2Z.
The Wren ·