Converse to Proposition 2.23 in Darmon, Diamond, Taylor's FLT Notes

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Can someone either prove or link me to a reference for Remark 2.24 (page 64) here? I am told that SGA7 covers this for general abelian varieties. I am wondering if a) anyone can pinpoint where in SGA7 this is covered, and b) if there is a less heavy reference that perhaps only covers this for elliptic curves. All needed definitions are on page 62 in the same document.