Under finiteness of the Tate-Shafarevich group and local Assumption 7.2, the normalized leading term at s=1 of the Hasse-Weil-Artin L-function of (A, chi) equals a product of a volume term, a ramification correction, a twisted regulator, and a characteristic ideal.
Curtis and Irving Reiner, Methods of representation theory
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On a Birch and Swinnerton-Dyer type conjecture for the Hasse-Weil-Artin $L$-functions in characteristic $p>0$
Under finiteness of the Tate-Shafarevich group and local Assumption 7.2, the normalized leading term at s=1 of the Hasse-Weil-Artin L-function of (A, chi) equals a product of a volume term, a ramification correction, a twisted regulator, and a characteristic ideal.