Invesco Galaxy Ethereum ETF (QETH) S-1/AIPO registration (amended)

Exhibit 5.1

MORRIS, NICHOLS, ARSHT & TUNNELLLLP

1201 NORTH MARKET STREET

P.O. BOX 1347

WILMINGTON, DELAWARE 19899-1347

(302) 658-9200

(302) 658-3989 FAX

June 21, 2024

Invesco Galaxy Ethereum ETF

3500 Lacey Road, Suite 700

Downers Grove, IL 60515

Ladies and Gentlemen:

We have acted as special Delaware counsel to Invesco Galaxy Ethereum ETF, a Delaware statutory trust (the “Trust”), in connection with certain matters of Delaware law relating to the issuance of Shares of the Trust. Capitalized terms used herein and not otherwise herein defined are used as defined in the Second Amended and Restated Declaration of Trust and Trust Agreement of the Trust dated on or about the date hereof (the “Governing Instrument”).

In rendering this opinion, we have examined and relied on copies of the following documents, each in the form provided to us: Pre-Effective Amendment No. 3 (the “Amendment”) to Registration Statement No. 333-274767 under the Securities Act of 1933, as amended, on Form S-1 of the Trust to be filed with the Securities and Exchange Commission on or about the date hereof; the Certificate of Trust of the Trust as filed in the Office of the Secretary of State of the State of Delaware (the “State Office”) on September 27, 2023; the Governing Instrument; the form of Participation Agreement to be entered into by the Sponsor and each Participant (as defined therein) (the “Form of Participant Agreement” and together with the Governing Instrument and the Amendment, the “Governing Documents”); and a Certificate of Sponsor of the Trust dated on or about the date hereof. In such examinations, we have assumed the genuineness of all signatures, the conformity to original documents of all documents submitted to us as copies or drafts of documents to be executed, and the legal capacity of natural persons to complete the execution of documents. We have further assumed for purposes of this opinion: (i) the due formation or organization, valid existence and good standing of each entity that is a signatory to any of the documents reviewed by us under the laws of the jurisdiction of its respective formation or organization; (ii) the due adoption, authorization, execution and delivery by, or on behalf of, each of the parties thereto (other than the Trust) of the above-referenced agreements, instruments, certificates and other documents and of all documents contemplated by the Governing Documents to be executed by Persons desiring to become Shareholders; (iii) that the activities of the Trust have been and will be conducted in accordance with the terms of the Governing Instrument and the Delaware Statutory Trust Act, 12 Del. C. §§ 3801 et seq. (the “Delaware Act”); (iv) that appropriate notation of the names and addresses of, the number of Shares held by, and the consideration paid by, Shareholders will be maintained in the appropriate registers and other books and records of the Trust in connection with the issuance or transfer of Shares; (v) that the required consideration for Shares is paid

Invesco Galaxy Ethereum ETF

June 21, 2024

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in accordance with the terms, conditions, requirements and procedures set forth in the Governing Documents and that the Shares are otherwise issued in accordance with the terms, conditions, requirements and procedures set forth in the Governing Documents and the Delaware Act; and (vi) that each of the documents examined by us is in full force and effect, expresses the entire understanding of the parties thereto with respect to the subject matter thereof and has not been amended, supplemented or otherwise modified, except as herein referenced. We have not reviewed any documents other than those identified above in connection with this opinion, and we have assumed that there are no documents, facts or circumstances that are contrary to, or inconsistent with the opinion expressed herein. No opinion is expressed herein with respect to the requirements of, or compliance with, federal or state securities or blue sky laws. Further, we express no opinion on the sufficiency or accuracy of any registration or offering documentation relating to the Trust or the Shares. As to any facts material to our opinion, other than those assumed, we have relied without independent investigation on the above-referenced documents and on the accuracy, as of the date hereof, of the matters therein contained.

Based on and subject to the foregoing, and limited in all respects to matters of Delaware law, it is our opinion that the Shares, when issued in accordance with the terms, conditions, requirements and procedures set forth in the Governing Documents, will constitute legally issued, fully paid and non-assessable shares of beneficial interest in the Trust.

We hereby consent to the filing of a copy of this opinion with the Securities and Exchange Commission as an exhibit to the Amendment. In giving this consent, we do not hereby admit that we come within the category of Persons whose consent is required under Section 7 of the Securities Act of 1933, as amended, or the rules and regulations of the Securities and Exchange Commission thereunder. This opinion speaks only as of the date hereof and is based on our understandings and assumptions as to present facts, and on the application of Delaware law as the same exist on the date hereof, and we undertake no obligation to update or supplement this opinion after the date hereof for the benefit of any Person (including any Shareholder) with respect to any facts or circumstances that may hereafter come to our attention or any changes in facts or law that may hereafter occur or take effect. This opinion is intended solely for the benefit of the Trust and the Shareholders in connection with the matters contemplated hereby and may not be relied upon by any other Person, or for any other purpose, without our prior written consent.