I have done a little research on this and there is, at least in English, a fine distinction to be draw between "joint", "several" and "solidary liabilities/obligaions".

The latin phrase “in solidum” is translated as “solidary” and occurs in relation to liabilities and obligations. English ‘solidary” is most often used in such contexts by itself without recourse to Latin, and in a wider range of applications. I could not find direct use of “solidary conviction” or “solidary sentence/sentencing” but some texts come quite close in associating the nature of a sentence with the solidary nature of the obligations of the defendants. E.g.:

Petitioner insists that by virtue of the clear wording of the statement, specifically the clause ". . . we jointly and severally agree and undertake . . .," and the concluding sentence on exhaustion, Chi's liability therein is solidary.
http://206.142.245.159/judjuris/juri1992/dec1992/gr_74886_19...

I therefore feel that it would be OK for the purposes of your translation to simply coin a phrase like “solidary conviction/sentence” because that already exists as a potential and intelligble phrase in English. This would be preferable to "in solidum conviction" because that Latin term is rare and not nearly so current as the equivalent "solidary" in legal contexts -- more people would be likely to understand you.

Below is some of the evidence – please ignore it if you think it is boring or of no interest to you:-

In solidum -- Latin term meaning for the whole. Where there are several co-obligants bound "in solidum", each is liable in full payment or performance, and the creditor may choose which of the obligants he will sue. Every person whose name appears on a bill, whether as acceptor or endorser, is liable in full payment of its contents although he may after payment do diligence against the others for relief. Those who in a joint obligation are not bound for the whole but only for their share are said to be liable "pro rata".
http://www.clickdocs.co.uk/glossary/in-solidum.htm

In solidum, liability see Solidary liability
http://www.lawlink.nsw.gov.au/lrc.nsf/pages/r89index

In other respects they are united, in that they treat of their common interests in a common council, and that the Cantons today attribute to themselves in Solidum a right of control over a canton that would undertake something against the common interest.
http://www.umanitoba.ca/faculties/arts/history/unionsavoy.ht...

What happens if my co-tenant doesn’t pay his share of the rent? --One of the main responsibilities of a co-tenant is to pay the rent. Sometimes, however, one co-tenant does not pay his share of the rent. Can the landlord ask you to pay the full rent in this case? It depends. If you are jointly liable for payment, the answer is no and, to the contrary, if the obligation is solidary, the answer is yes. If you are jointly liable, then each co-tenant is only responsible for his share of the total rent. For example, Christine and Stephanie sign a lease together. If the rent is $600 and Christine does not pay, Stephanie cannot be asked to pay more than $300. Where the obligation is joint, the lease may not necessarily contain a distinct clause to this effect.
http://www.educaloi.qc.ca/TLR_Law/F01A_Capsules/index.php3?n...

Ñîëèäàðíîå îáÿçàòåëüñòâî
Ñîëèäàðíàÿ îòâåòñòâåííîñòü
Joint responsibility; Solidary responsibility
Ñîëèäàðíîå îáÿçàòåëüñòâî - îáÿçàòåëüñòâî ñ ìíîæåñòâåííîñòüþ ëèö, êîòîðîå ìîæåò âîçíèêíóòü êàê íà ñòîðîíå äîëæíèêà, òàê è íà ñòîðîíå êðåäèòîðà.
http://www.glossary.ru/cgi-bin/gl_sch2.cgi?R1dRurtl,tg9!wgko...

BILL C-47 (As passed by the House of Commons) ... of the duty, interest or other amount shall discharge the joint and several or solidary ... (a) on conviction on indictment, to a fine of not less than $50,000 and ...
http://www.parl.gc.ca/37/1/parlbus/chambus/house/bills/gover...

I hope that helps.


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Note added at 2002-08-05 07:37:23 (GMT)
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P.S. \"joint and several\" responsibility (i.e. both) can be equated with \"solidary\" responsibility -- but it may be that \"joint\" (by itself) and \"several\" (by itself) have distinct meanings -- a \"pro rata\" liability in the first case, and I\'m not sure what in the second case.

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Note added at 2002-08-05 07:37:23 (GMT)
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P.S. \"joint and several\" responsibility (i.e. both) can be equated with \"solidary\" responsibility -- but it may be that \"joint\" (by itself) and \"several\" (by itself) have distinct meanings -- a \"pro rata\" liability in the first case, and I\'m not sure what in the second case.

I can't find any reliable references for "solidary conviction" or "in solidum conviction," but I do find "solidary judgment" used by courts in Canada and in Louisiana, both places where there is an overlap between French-based statutory law and Anglo case law. The problem with using "conviction" here is that "conviction" is the penalty imposed in criminal cases; no one is convicted in civil cases; rather a *judgment* is rendered against one of the parties.