In the paper "Effective Chabauty" by Robert Coleman, there is one proposition:
Let C be a curve of genus two over $\mathbb{Q}$, with rank of its Jacobian at most 1. (1) If C has good reduction at 2 or 3, then $\#C(\mathbb{Q})\leq 12$. (2) If C has good reduction at 3 and has 4 rational hyperbolic branch points, then $\#C(\mathbb{Q})\leq 6$.
There is one example, with curve $C:y^2=x(x^2-1)(x-\lambda)(x^2+ax+b)$, such that $a,b\in\mathbb{Z}$ and $ord_3(\lambda)<0$ and divisible by 2. Also suppose that $3\nmid b(1+a+b)(1-a+b)$. Then C has good reduction modulo 3.
How can I determine reduction modulo 3 when the curve do not have all integer coefficients, especially when denominator of some coefficient is divisible by 3? How can I check whether C has good reduction modulo 3?
Also, is there any example of curve with good reduction at 2 with 12 rational points and rank of its Jacobian less or equal to 1?
Thank you in advance.