Title: On the Birch--Swinnerton-Dyer conjecture at reducible primes of good and bad multiplicative reduction Abstract: We report on work in progress with Mulun Yin. Castella--Gross--Lee--Skinner recently proved Perrin-Riou's Heegner point main conjecture for RM abelian varieties at primes p of good reduction for which the mod-p Galois representation rho_p is reducible. They have the restriction that the characters in the semisimplification of rho_p are non-trivial. We work on removing this restriction and generalize the result to newforms of higher weight, allowing us to also treat bad multiplicative reduction. As a consequence, we get the p-part of the Birch--Swinnerton-Dyer conjecture for analytic rank 1 and a p-converse theorem.