  Extending the former work for the good reduction case, we provide a numerical
criterion to verify a large portion of the "Iwasawa main conjecture without
$p$-adic $L$-functions" for elliptic curves with additive reduction at an odd
prime $p$ over the cyclotomic $\mathbb{Z}_p$-extension. We also deduce the
corresponding $p$-part of the Birch and Swinnerton-Dyer formula for elliptic
curves of rank zero from the same numerical criterion. We give explicit
examples at the end and specify our choice of Kato's Euler system in the
appendix.

Number Theory